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Chapter 11: Problem 124

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

Short Answer

Expert verified
The solution to the quadratic equation \(x^{2}+6x+8=0\) by completing the square is \(x=-4, -2\).

Step by step solution

01

Arrange the Equation

First, rearrange the equation to the form \(x^2+bx=c\). For this, isolate \(x^2\) and the \(x\)-term on one side, and the constant on the other side of equation. In this case, our equation is already in the correct form: \(x^2+6x+8=0\).
02

Complete the Square

Next, complete the square by adding and subtracting \((b/2)^2\) inside the parentheses on the left side of the equation. Here, \(b = 6\), so we add \((6/2)^2 = 9\) to and subtract it from the left side of the equation. The equation becomes \(x^2+6x+9-9+8=0\), which simplifies to \((x+3)^2-1=0\). Thus, we have completed the square.
03

Solve for \(x\)

Lastly, solve for \(x\) by first isolating \((x+3)^2\) on one side of the equation, giving us \((x+3)^2=1\). Then take square root of both sides to solve for \(x\), giving \(x+3=卤1\). Thus, our solutions are \(x=-3卤1\), which further simplifies to \(x=-4, -2\).

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