Question

(x-2) (x+9)= 4x solve and check solution

Answer 1

x = -6 and x=3

Explanation:

We have been given the equation to solve

`(x-2)(x+9)=4x`

Let us simplify the left hand side of the equation using FOIL (first outer in last).

`x^2+9x-2x-18=4x\\\\x^2+7x-18=4x\\\\x^2+3x-18=0`

Now, let us find the factors using AC method.

Middle term 3x can be written as 6x - 3x

`x^2+3x-18=0\\\\x^2+6x-3x-18=0\\\\x(x+6)-3(x+6)=0\\\\(x+6)(x-3)=0\\\\x=-6,3`

Now, let us check the solution by plugging values in the original equation

For x= -6

`(-6-2)(-6+9)=4(-6)\\\\(-8)(3)=-24\\\\-24=-24\Rightarrow\text{ True}`

Thus, x=-6 is a solution.

For x= 3

`(3-2)(3+9)=4(3)\\\\(1)(12)=12\\\\12=12\Rightarrow\text{ True}`

Thus, x=3 is a solution.

Therefore, the solutions are x = -6 and x=3