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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 quadratic equation \(x^{2}+6 x+8=0\) are \(x=-2\) and \(x=-4\).

Step by step solution

01

Determine the Coefficients

Identify the coefficients in the standard form \(ax^2 + bx + c = 0\). In the equation \(x^2 + 6x + 8=0\), \(a=1\), \(b=6\), and \(c=8\).
02

Substitute the values into Quadratic Formula

Substitute these coefficients \(a\), \(b\), and \(c\) into the quadratic formula \(x= -b \pm \sqrt{b^2-4ac} / 2a\). This will result in \(x= -6 \pm \sqrt{6^2-4(1)(8)} / 2(1)\).
03

Simplify under the square root

Calculate the expression under the square root, \(b^2-4ac\), which becomes \(36-32\). This simplifies to \(\sqrt{4}\). Hence, the equation will now look like \(x= -6 \pm \sqrt{4} / 2\).
04

Continue simplification

Simplify \(\sqrt{4}\) to \(2\). The equation will now look like \(x= -6 \pm 2 / 2\).
05

Calculate The Roots

Next, solve for \(x\) for the plus and minus cases separately. The roots will be \(x= (-6+2)/2=-2\) and \(x= (-6-2)/2=-4\).

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