Question

Solve the following showing all steps. (x+6)2=8​

Answer 1

Expanding the left-hand side of the equation, we get:

(x+6)2 = (x+6)(x+6) = x(x+6) + 6(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36

So now we have the equation:

x^2 + 12x + 36 = 8

Subtracting 8 from both sides, we get:

x^2 + 12x + 28 = 0

We can factor this quadratic equation as:

(x+2)(x+14) = 0

This gives us two possible solutions:

x+2 = 0, so x = -2

x+14 = 0, so x = -14

Therefore, the solutions to the equation (x+6)2 = 8 are x = -2 and x = -14.

Answer 2

Explanation:

Here is one way :

(x+6)^2 = 8 Take the square root of both sides

x+6 = +- sqrt 8

x = -6 +- sqrt8 = -6 + 2 sqrt 2 or -6 - 2 sqrt 2 = - 3.17 or - 8.83