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

1 Answer
Feb 5, 2016

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