MATH SOLVE

5 months ago

Q:
# Using complete square to slove for x in the equation (x+7) (x-9)=25

Accepted Solution

A:

Answer: [tex]x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]Step-by-step explanation: Apply Distributive property: [tex](x+7)(x-9)=25\\\\x^2-9x+7x-63=25[/tex] Add like terms and then add 63 to both sides of the equation: [tex]x^2-2x-63=25\\\\x^2-2x-63+63=25+63\\\\x^2-2x=88[/tex] Pick the coefficient of the x term, divide it by 2 and square it: [tex](\frac{2}{2})^2=1[/tex] Add it to both sides of the equation: [tex]x^2-2x+1=88+1[/tex] Rewriting the left side as a squared binomial, we get: [tex](x-1)^2=89[/tex] Apply square root to both sides: [tex]\sqrt{(x-1)^2}=\±\sqrt{89}\\\\x-1=\±\sqrt{89}[/tex] And finally we need to add 1 to both sides of the equation. Then we get: [tex]x-1+1=\±\sqrt{89}+1\\\\x=\±\sqrt{89}+1\\\\\\x_1=1+\sqrt{89}\\\\x_2=1-\sqrt{89}[/tex]