Question

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

Answer 1

Given the equation:

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

Then;

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

Using the distributive property,
`a \cdot (b+c) = a\cdot b + a\cdot c`

`x^2-9x+7x-63 =25`

Combine like terms;

`x^2-2x-63 =25`

Subtract 25 from both sides we have;

`x^2-2x-88=0`

Using completing square form:

Add and subtract
`((2)/(2))^2 =1` we have;

`x^2-2x-88+1-1=0`

⇒
`(x-1)^2-89 = 0`

Add 89 to both sides we have;

⇒
`(x-1)^2=89`

Taking square root both sides we get;

`x-1 = \pm √(89)`

Add 1 to both sides we have;

`x = 1 \pm √(89)`

Therefore, the values of x are:

`1+√(89)` and
`1 -√(89)`