Question

Use completely the square to solve for x in the equation (x+7)(x-9)=25

Answer 1

You mean "completing the square," don't you? ;)

(x+7)(x-9)=25 can be expanded: x^2 - 9x + 7x - 63 + 25, which becomes

x^2 -2x = 38.

Let's now complete the square:

x^2 - 2x + (1)^2 - (1)^2 = 38, or x^2 - 2x + 1 = 39

Rewrite that as (x-1)^2 = 39

Take the sqrt of both sides: x-1 = plus or minus sqrt(39)

Write the roots: x = 1+sqrt(39) and x = 1 = sqrt(39) (answers)

Answer 2

Answer with Step-by-step explanation:

we are given a equation:

(x+7)(x-9)=25

⇒ x(x-9)+7(x-9)=25

⇒ x²-9x+7x-63=25

⇒ x²-2x=25+63

⇒ x²-2x=88

adding 1 on both sides

⇒ x²-2x+1=88+1

⇒ (x-1)²=89

⇒
`x-1=√(89)\ or\ x-1=-√(89)`

⇒
`x=√(89)+1\ or\ x=-√(89)+1`

Hence, value of x are:

`x=√(89)+1\ or\ x=-√(89)+1`