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Chapter 11: Problem 36

Solve each quadratic equation by completing the square. $$x^{2}+6 x=7$$

Short Answer

Expert verified
The solutions of the equation \(x^{2}+6 x=7\) are \(x = 1, -7\)

Step by step solution

01

Rearrange the Equation

Rearrange the equation to make the first two terms one side and the constant term on another side. So, the equation becomes: \(x^{2} + 6x - 7 = 0\)
02

Complete the Square

To complete the square, we need to add square of half of the coefficient of x to both sides. Half of 6 is 3, so we add 3^2 = 9 to both sides. The equation then becomes: \(x^{2} + 6x + 9 = 7 + 9\)
03

Write as The Square of A Binomial

This creates a perfect square trinomial on the left, which can be written as the square of a binomial. The equation becomes: \((x+3)^{2} = 16\)
04

Solve for X

Take square root on both sides to solve for x. We get two solutions, because the square root of \(16\) is either \(4\) or \(-4\). So,\(x+3 = 4\) and \(x+3 = -4\). The solutions are \(x = 4 - 3 = 1\) or \(x = -4 - 3 = -7\)

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