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Chapter 0: Problem 70

Solve each quadratic equation by completing the square. $$x^{2}+4 x=12$$

Short Answer

Expert verified
The solutions to the quadratic equation are \(x = 2\) and \(x = -6\).

Step by step solution

01

Write the quadratic equation

The given equation is \(x^{2}+4 x=12.\)
02

Rearrange the equation

To facilitate completing the square, rearrange the equation to bring the constant term to the other side: \(x^2 + 4x -12 = 0.\)
03

Complete the square

Take the coefficient of the \(x\) term, divide it by two and square it i.e., \(\left(\frac{4}{2}\right)^2 =4\). Add this value to both sides of the equation to formulate a trinomial square on the left: \(x^2 + 4x + 4 = 12 + 4.\) This results in \((x+2)^2 = 16.\)
04

Solve for \(x\)

Take the square root of both sides, remembering both the positive and negative roots, to find the solutions for \(x\): \(x+2 = 卤 \sqrt{16}\). This results in \(x = -2 卤 4\).

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Most popular questions from this chapter

Describe the solution set of \(|x|>-4\)

Perform the indicated operations. Simplify the result, if possible. $$\left(4-\frac{3}{x+2}\right)\left(1+\frac{5}{x-1}\right)$$

What is the discriminant and what information does it provide about a quadratic equation?

Perform the indicated operations. Simplify the result, if possible. $$\frac{1}{x^{2}-2 x-8} \div\left(\frac{1}{x-4}-\frac{1}{x+2}\right)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I subtracted \(\frac{3 x-5}{x-1}\) from \(\frac{x-3}{x-1}\) and obtained a constant.
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