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Chapter 11: Problem 91

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 a, b, and c

In the equation \(x^{2}+6 x+8=0\), \(a = 1\), \(b = 6\) and \(c = 8\). These values correspond to the coefficients of the quadratic polynomial.
02

Substitute a, b and c into the quadratic formula

Now substitute \(a = 1\), \(b = 6\) and \(c = 8\) into the quadratic formula \(-\frac{b \pm \sqrt{b^{2}-4ac}}{2a}\). This gives us \(-\frac{6 \pm \sqrt{(6)^{2}-4*1*8}}{2*1}\) which simplifies to \(-\frac{6 \pm \sqrt{36-32}}{2}\)
03

Solve the equation

Solving the equation \(-\frac{6 \pm \sqrt{36-32}}{2}\) gives us \(-\frac{6 \pm \sqrt{4}}{2}\). This can be simplified to \(-\frac{6 \pm 2}{2}\). This gives two results: \(\frac{-6 + 2}{2} = -2\) and \(\frac{-6 - 2}{2} = -4\). So, the solutions of the equation are \(x = -2\) and \(x = -4\).

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