Question

Use completing the square to solve for x in the equation (x 7) (x minus 9) = 25.

Answer 1

The values of $x$ are $1+\sqrt{89}$ and $1-\sqrt{89}$.

To find the values of x:

Given equation: $(x+7)(x-9)=25$

Then: $x(x-9)+7(x-9)=25$

Using the distributive property: $a.(b+c)=a.b+a.c$

$x^{2} -9x+7x-63=25$

Combine like terms:

$x^{2} -2x-63=25$

Subtract 25 from both sides and obtain:

$x^{2} -2x-88=0$

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 roots on both sides, obtain:

$x-1=$ ± $\sqrt{89}$

Add 1 to both sides we have:

$x=1$±$\sqrt{89}$

Therefore, the values of $x$ are $1+\sqrt{89}$ and $1-\sqrt{89}$.

Know more about square roots here:

brainly.com/question/428672

#SPJ4

The complete question is given below:

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