Question

How do you solve the equation `x^2+8x+16=7` by completing the square?

Answer 1

`color(indigo)(x = sqrt7 - 4`, `color(maroon)(x = -sqrt7 - 4`

Explanation:

`x^2 + 8x + 16 = 7`

`(x+a)^2 = x^2 + 2ax + a^2`

`:. L H S = x^2 + 2*4*x + 4^2 = (x+4)^2`

Hence, `(x+4)^2 = 7`

`x+4 = +- sqrt7`, taking root on both sides

`color(maroon)(x = +-sqrt7 - 4`