Question

How do you complete the square to solve `x^2+6x=7`?

Answer 1

`x^2 + 6x = 7`
To write the Left Hand Side as a Perfect Square, we add 9 to both sides
`x^2 + 6x + 9= 7+ 9`
`x^2 + 2*3*x + 3^2 = 16`
Using the Identity `color(blue)((a+b)^2 = a^2 + 2ab + b^2`, we get
`(x+3)^2 = 16`
`x + 3 = +sqrt16` or `x +3 = -sqrt16`
`x =4-3or x = -4 - 3`
`color(green)(x = 1 or color(green)(x = -7`