Problem 158 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify coefficients a, b, and c

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

Step 2: 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 \(x = \frac{-6 \pm \sqrt{6^{2}-4(1)(8)}}{2(1)}\).

Step 3: Simplify under the square root

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

Step 4: Simplify the formula

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

Step 5: 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.