Question

Solve the equation for the variable:

1.) x^2 - 12x = 45

2.) x^2 - 6x = 7

Answer 1

1. )

`x^(2) -12x=45\\x^(2) -12x-45 = 0\\(x-15)(x+3) = 0\\x = -3, 15`

2. )

`x^(2)-6x=7\\x^(2) -6x-7=0\\(x-7)(x+1) = 0\\x = -1, 7`

Answer 2

Given Below.

Step-by-step explanation:

(a)

`x^2 - 12x = 45`

`x^2 - 12x -45 = 0`

`x^2 - 15x + 3x - 45 = 0`

`x ( x-15) + 3 ( x - 15) = 0`

`(x+3)(x-15) = 0`

`x = -3 , 15`

(b)

`x^2 - 6x = 7`

`x^2 - 6x -7 = 0`

`x^2-7x + x -7 = 0`

`x(x-7)+1(x-7) = 0`

`(x+1)(x-7) =0`

`x = -1, 7`