Find the solution(s) using the quadratic formula. 4 ( x − 2 ) 2 − 5 = x + 7 4\left(x-2\right)^2-5=x+7

Here, we want to solve the quadratic four times x minus two squared minus five equals x plus seven using the quadratic formula. Now first, we've got a couple steps before we can actually apply our quadratic formula. We need to get this in standard form. So in order to do that, we need to foil out all of our parentheses and then combine all of our like terms. So let's start with x minus two squared. I can rewrite that as x minus two times x minus two. And then using our foil technique, we'd have x times x is x squared, x times negative two, negative two x, Negative two times x, another negative two x. And negative two times negative two makes positive four. So combining like terms, we get x squared minus four x plus four. So now I'm going to take this and plug it back into my original equation, and we'll have four times x squared minus four x plus four minus five equals x plus seven. Next, let's distribute in this four into this quadratic. Doing that, we get four x squared minus 16 x plus 16 minus five equals x plus seven. Now we're going to combine some like terms of 16 and negative five. So we have four x squared minus 16 x plus 11 equals x plus seven. And now let's subtract x and seven over to the other side of our equation and combine like terms. So I'll get four x squared, negative 16 x minus x will give us negative 17 x, so minus 17 x. And positive 11 minus seven will combine to make positive four, so we'll have plus four. And that is now all equal to zero. So now that we have a quadratic in standard form, we can apply our quadratic formula. So let's identify our a value as four, our b value as negative 17, and our c value as also four. And plug these in. So we'll get x is equal to negative b, so negative 17, plus or minus square root of b squared, so negative 17 squared, minus four times a, which is four, times c, which is four, all divided by two times a, which is four. Simplifying, we'll have x is equal to negative negative 17, so positive 17, plus or minus negative 17 squared. Using our calculator, we can find is 289 minus four times four times four, also using our calculator, gets us 64. Now we'll all be divided by two times four, which is eight. Now 289 minus 64 is two twenty five, which is a perfectly square number. So this will reduce to x is equal to 17 plus or minus the square root of two twenty five, which is 15, all divided by eight. And now we have our two solutions. We have x is equal to 17 plus 15, which is 32 divided by eight. And that simplifies to 32 divided by eight, which is four. And our second solution is 17 minus 15. So we have x equals two divided by eight, and that simplifies to x equals one fourth. So these are the two solutions to this quadratic equation. We could always check our work by taking these solutions and plugging them back in to make sure the equation is true.

Skip topic navigation

1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving43m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
21m

Translating Sentences to Algebraic Equations
2m

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics22m

Tables

Bar Graphs
3m

Frequency Distributions and Histograms
5m

Line Graphs
9m

Circle Graphs
4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

Ellipses
35m

Hyperbolas
41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

19. Quadratic Equations and Functions

The Quadratic Formula

Prealgebra, Beginning Algebra, & Intermediate Algebra

19. Quadratic Equations and Functions

The Quadratic Formula

이전 문제다음 문제

Prealgebra, Beginning Algebra, & Intermediate Algebra 때문에 힘들어하고 계신가요?

저희를 신뢰하는 수천 명의 학생들이 시험 합류하세요!

객관식

Find the solution(s) using the quadratic formula.
$4 {(x - 2)}^{2} - 5 = x + 7$

$x=5,x=$\frac$12$

$x=5,x=$\frac$14$

$x=4,x=$\frac$14$

$x=4,x=$\frac$12$

0 댓글

이전 문제다음 문제

3:45m

다음 시청

마스터 Choosing a Method to Solve Quadratic Equations가 Patrick Ford 짧은 영상으로 설명해 줍니다

Prealgebra, Beginning Algebra, & Intermediate Algebra 때문에 힘들어하고 계신가요?

Find the solution(s) using the quadratic formula.4(x−2)2−5=x+74\(\left\)(x-2\(\right\))^2-5=x+7

다음 시청

Find the solution(s) using the quadratic formula.
$4 {(x - 2)}^{2} - 5 = x + 7$