Question

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

Answer 1

x = 1; x = -7

Explanation:

Given

x^2 + 6x = 7

we want to complete the square. If we have (x + a)^2 and expand it we get: x^2 + 2ax + a^2. The second term in the equation suggest that 2ax = 6x or a = 3. Then, adding 3^2 at both sides of the equation of the problem:

x^2 + 6x + 3^2 = 7 + 3^2

(x + 3)^2 = 16

x + 3 = sqrt(16)

That gives us two options

x + 3 = 4

x = 1

or

x + 3 = -4

x = -7

Answer 2

so first you have to find the perfect square that matches up with x^2 + 6x

so half of 6, and square it. your perfect square is 9

x^2 + 6x + 9 = 7 + 9

then, condense the left side of the equation into a squared binomial:

(x + 3)^2 = 16

take the square root of both sides:

x + 3 = ± √16

therefore:

x + 3 = ± 4

x = - 3 ± 4

so your solution set is:

x = 1, -7