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Chapter 1: Problem 158

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

Short Answer

Expert verified
The solutions to the equation \(x^{2}+6 x+8=0\) are \(x=-2\) and \(x=-4\).

Step by step solution

01

Identify coefficients a, b, and c

From \(x^{2}+6 x+8=0\), we can identify that a=1, b=6, and c=8.
02

Substitute the values into the quadratic formula

Substitute the values of a, b, and c into the quadratic formula. So, \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\) becomes \(x = \frac{-6 \pm \sqrt{6^{2}-4(1)(8)}}{2(1)}\).
03

Simplify under the square root

The expression under the square root is \(6^{2}-4(1)(8)\), which simplifies to \(36 - 32 = 4\).
04

Simplify the formula

After simplifying, the quadratic formula becomes \(x = \frac{-6 \pm \sqrt{4}}{2}\).
05

Calculate the roots

This simplifies to two answers, \(x = \frac{-6 + 2}{2} = -2\) and \(x = \frac{-6 - 2}{2} = -4\). These are the two roots of the quadratic equation.

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Most popular questions from this chapter

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(1-\frac{x}{2}>4\)

Solve absolute value inequality. \(|x|>3\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(1-\frac{x}{2}>4\)

This will help you prepare for the material covered in the next section. Is \(-1\) a solution of \(3-2 x \leq 11 ?\)

Solve compound inequality. \(6< x+3<8\)
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