Question

Solve the equation, eliminating any extraneous solutions. x2 5(x 5)=30(x 5)

Answer 1

X^2+5(x+5)=30(x+5)
distribue
x^2+5x+25=30x+150
minus 30x+150 from both sides
x^2-25x-125=0
use quadratic formula
in form
ax^2+bx+c=0
x=$\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

a=1
b=-25
c-125

x=$\frac{-(-25)+/- \sqrt{(-25)^2-4(1)(-125)} }{2(1)}$
x=$\frac{25+/- \sqrt{625+500} }{2}$
x=$\frac{25+/- \sqrt{1125} }{2}$
x=$\frac{25+/- 15\sqrt{5} }{2}$
x=12.5+/- 7.5√5

x=12.5+7√5 or 12.5-7.5√5
no extranious roots seen