Question

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

Answer 1

The answer is C..

x=1+/- the square root of 89

Answer 2

Answer:

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 $(\frac{2}{2})^2 =1$ 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;

$x-1 = \pm \sqrt{89}$

Add 1 to both sides we have;

$x = 1 \pm \sqrt{89}$

Therefore, the values of x are:

$1+\sqrt{89}$ and  $1 -\sqrt{89}$