Question

Using complete square to slove for x in the equation (x+7) (x-9)=25

Answer 1

`x_1=1+√(89)\\\\x_2=1-√(89)`

Explanation:

Apply Distributive property:

`(x+7)(x-9)=25\\\\x^2-9x+7x-63=25`

Add like terms and then add 63 to both sides of the equation:

`x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88`

Pick the coefficient of the x term, divide it by 2 and square it:

`((2)/(2))^2=1`

Add it to both sides of the equation:

`x^2-2x+1=88+1`

Rewriting the left side as a squared binomial, we get:

`(x-1)^2=89`

Apply square root to both sides:

`√((x-1)^2)=\±√(89)\\\\x-1=\±√(89)`

And finally we need to add 1 to both sides of the equation. Then we get:

`x-1+1=\±√(89)+1\\\\x=\±√(89)+1\\\\\\x_1=1+√(89)\\\\x_2=1-√(89)`