Question

PLEASE HELP!!!!

Solve for when f(x)=g(x)
f(x)=5x
g(x)=x^2-10x+1

Answer 1

`\large\boxed{x=(15-√(221))/(2)\ or\ x=(15+√(221))/(2)}`

Explanation:

`f(x)=5x\\\\g(x)=x^2-10x+1\\\\f(x)=g(x)\to5x=x^2-10x+1\qquad\text{subtract 5x from both sides}\\\\x^2-15x+1=0\\\\\text{Use the quadratic formula}:\\\\ax^2+bx+c=0\\\\x=(-b\pm√(b^2-4ac))/(2a)\\\\a=1,\ b=-15,\ c=1\\\\b^2-4ac=(-15)^2-4(1)(1)=225-4=221\\\\x=(-(-15)\pm√(221))/(2(1))=(15\pm√(221))/(2)`