Question

Solve for x

(X^2-5x)=(9x-12)

Answer 1

x = 13.08 or 0.917

Explanation:

`x^(2) -5x=9x-12`

First, subtract 9x by both sides.

`x^(2) -5x-9x=-12\\x^(2) -14x=-12`

And now we can use completing square method to solve for x.

`x^(2) -14x=-12`

Add (14/2)² to both sides of the equation.

`x^(2) -14x+(14/2)^(2) =-12+(14/2)^(2) \\\\x^(2) -14x+49=-12+49\\\\x^(2) -14x+49=37`

Factor the left side of the equation into a perfect square.

`(x-7)^(2) =37`

Square root both sides of the equation and solve for x.

`x-7=\±√(37)`

Add 7 to both sides.

`x = \±√(37) +7`

Therefore,

x = √37 + 7

x = 13.08

or

x = -√37 + 7

x = 0.917