The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
To find the values of x:
Given equation: [tex](x+7)(x-9)=25[/tex]
Then: [tex]x(x-9)+7(x-9)=25[/tex]
Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]
[tex]x^{2} -9x+7x-63=25[/tex]
Combine like terms:
[tex]x^{2} -2x-63=25[/tex]
Subtract 25 from both sides and obtain:
[tex]x^{2} -2x-88=0[/tex]
Using completing square form:
Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:
[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]
Add 89 to both sides we have:
[tex](x-1)^{2} =89[/tex]
Taking square roots on both sides, obtain:
[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]
Add 1 to both sides we have:
[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]
Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
Know more about square roots here:
https://brainly.com/question/428672
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The complete question is given below:
Use completing the square to solve (x + 7)(x – 9) = 25 for x.
