Domanda del libro di testo
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 77
Solve each equation by the method of your choice.
Guida verificata passo dopo passo1
Start with the given equation: \( (x-3)^2 - 25 = 0 \).
Isolate the squared term by adding 25 to both sides: \( (x-3)^2 = 25 \).
Take the square root of both sides, remembering to consider both the positive and negative roots: \( x - 3 = \pm \sqrt{25} \).
Simplify the square root: \( x - 3 = \pm 5 \).
Solve for \(x\) by adding 3 to both sides for each case: \( x = 3 + 5 \) and \( x = 3 - 5 \).
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Solving Quadratic Equations
Quadratic equations are polynomial equations of degree two, typically in the form ax² + bx + c = 0. Solving them involves finding values of x that satisfy the equation. Common methods include factoring, completing the square, and using the quadratic formula.
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06:08
Solving Quadratic Equations by Factoring
Difference of Squares
The difference of squares is a special factoring technique where an expression of the form a² - b² can be factored into (a - b)(a + b). Recognizing this pattern simplifies solving equations like (x - 3)² - 25 = 0 by rewriting 25 as 5².
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06:24Solving Quadratic Equations by Completing the Square
Isolating the Variable
Isolating the variable means manipulating the equation to get x alone on one side. This often involves adding, subtracting, multiplying, dividing, or taking roots. It is a fundamental step in solving equations to find the exact values of the unknown.
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05:28Equations with Two Variables
Pratica correlata
Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5
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Domanda del libro di testo
Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).
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Domanda del libro di testo
In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.
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Domanda del libro di testo
The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|
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Domanda del libro di testo
In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.
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