How do you solve 6x ^ { 2} - 36= - 6x?

1 Answer
Oct 9, 2017

See a solution process below: x = -3 and x = 2

Explanation:

First, put the equation in standard form:

6x^2 + color(6x) - 36 = -6x + color(6x)

6x^2 + 6x - 36 = 0

We can now use the quadratic equation to solve this problem:

The quadratic formula states:

For color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0, the values of x which are the solutions to the equation are given by:

x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))

Substituting:

color(red)(6) for color(red)(a)

color(blue)(6) for color(blue)(b)

color(green)(-36) for color(green)(c) gives:

x = (-color(blue)(6) +- sqrt(color(blue)(6)^2 - (4 * color(red)(6) * color(green)(-36))))/(2 * color(red)(6))

x = (-color(blue)(6) +- sqrt(36 - (-864)))/12

x = (-color(blue)(6) +- sqrt(36 + 864))/12

x = (-color(blue)(6) - sqrt(900))/12 and x = (-color(blue)(6) + sqrt(900))/12

x = (-color(blue)(6) - 30)/12 and x = (-color(blue)(6) + 30)/12

x = -36/12 and x = 24/12

x = -3 and x = 2

Another way of solving this quadratic equation:

6x^2+6x-36=0

(3x+9)(2x-4)=0

3x must be -9 or 2x must be 4 to end up with 0.

3x=-9
x=-3

2x=4
x=2

Therefor x=-3 or x=2