Question

How do you solve `(x-4)(x+3) = 6`?

Answer 1

`x= (1+-sqrt(73))/2`

Explanation:

How to solve `(x-4)(x+3) = 6`

Step 1: Multiple the expand and combine like terms for the left side of the equation

`(x-4)(x+3) = 6`

`(x^2-4x+3x-12)= 6`

`(x^2-x+-2) = 6`

Step 2-Set the equation equal to zero by subtracting both side of the equation by 6

`x^2 -x-12= 6`

`-6 " " " -6`
`=====`
`color(red)(x^2 -x -18= 0`

Step 3 Solve the equation using quadratic formula, since we can't factor it

Recall: Quadratic formula: `x= (-b+- sqrt((b)^2-4ac))/(2a)`

`color(red)(x^2 -x -18= 0`

`a = 1, b = -1, c= -18`

Substitute into the quadratic formula, we get
`x= (-(-1)+- sqrt((-1)^2-4(1)(-18)))/(2(1)`

`x= (1+-sqrt(1+72))/(2)`

`x= (1+-sqrt(73))/2`