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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 50
Chapter 2, Problem 50

Solve each equation in Exercises 47–64 by completing the square. x2+4x=12 x^2 + 4x = 12

Verified step by step guidance
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Start with the given equation: \(x^2 + 4x = 12\).
To complete the square, first move the constant term to the other side: \(x^2 + 4x = 12\) (already isolated).
Take half of the coefficient of \(x\), which is 4, so half is \(\frac{4}{2} = 2\), then square it: \(2^2 = 4\).
Add this square (4) to both sides of the equation to maintain equality: \(x^2 + 4x + 4 = 12 + 4\).
Rewrite the left side as a perfect square trinomial: \((x + 2)^2 = 16\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Completing the Square

Completing the square is a method used to solve quadratic equations by transforming the equation into a perfect square trinomial. This involves adding a specific value to both sides of the equation to create a binomial squared, making it easier to solve for the variable.
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Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0. Understanding its structure is essential for applying methods like completing the square, factoring, or using the quadratic formula to find the roots.
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Isolating the Variable

Isolating the variable involves rearranging the equation so that the variable term is alone on one side. This step is crucial before completing the square, as it allows you to manipulate the equation properly and solve for the unknown.
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Equations with Two Variables
Related Practice
Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 1/(x - 1) + 5 = 11/(x - 1)

Textbook Question

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is three decreased by the square of the x-value.

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Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = C/(1 - r) for r

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Textbook Question

Perform the indicated operations and write the result in standard form. (7-i)(2+3i)

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Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

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Textbook Question

Perform the indicated operations and write the result in standard form. −8(−3−−5)\(\sqrt{-8}\) \(\left\)( \(\sqrt{-3}\) - \(\sqrt{-5}\) \(\right\))

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