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=
`(-b+/- √(b^2-4ac) )/(2a)`

a=1
b=-25
c-125

x=
`(-(-25)+/- √((-25)^2-4(1)(-125)) )/(2(1))`
x=
`(25+/- √(625+500) )/(2)`
x=
`(25+/- √(1125) )/(2)`
x=
`(25+/- 15√(5) )/(2)`
x=12.5+/- 7.5√5

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