Domanda del libro di testo
Solve each radical equation in Exercises 88–89. √ (2x-3) + x = 3
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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 87
Solve each equation in Exercises 83–108 by the method of your choice.
Guida verificata passo dopo passo1
Start with the given equation: \(3x^2 = 60\).
Isolate the \(x^2\) term by dividing both sides of the equation by 3: \(x^2 = \frac{60}{3}\).
Simplify the right side to get \(x^2 = 20\).
To solve for \(x\), take the square root of both sides: \(x = \pm \sqrt{20}\).
Simplify the square root if possible to express the solution in simplest radical form.
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Solving Quadratic Equations
A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solving such equations involves finding the values of x that satisfy the equation. Methods include factoring, completing the square, using the quadratic formula, or isolating the variable when possible.
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Solving Quadratic Equations by Factoring
Isolating the Variable
Isolating the variable means manipulating the equation to get the variable alone on one side. This often involves performing inverse operations such as division, multiplication, addition, or subtraction. For example, dividing both sides by the coefficient of x² helps simplify the equation before solving.
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05:28Equations with Two Variables
Square Roots and Their Properties
When an equation involves x², taking the square root of both sides can help solve for x. Remember that both positive and negative roots must be considered, since (±√a)² = a. Understanding how to apply square roots correctly is essential for solving quadratic equations without linear terms.
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02:20Imaginary Roots with the Square Root Property
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The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)
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Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|
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Domanda del libro di testo
Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2
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Domanda del libro di testo
In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).]
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Domanda del libro di testo
In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).]
a)b)c)d)e)f)
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