Question

Solve the equation x+x(2x-5)=23

Answer 1

`\large\boxed{1\pm2.5\sqrt2}`

Explanation:

`x+x(2x-5)=23\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\x+2x^2-5x=23\qquad\text{combine like terms}\\\\2x^2+(x-5x)=23\\\\2x^2-4x=23\qquad\text{subtract 23 from both sides}\\\\2x^2-4x-23=0\\\\\text{use the quadratic formula for a quadratic trinomial:}\ ax^2+bx+c=0\\\\x=(-b\pm√(b^2-4ac))/(2a)\\\\a=2,\ b=-4,\ c=-23\\\\x=(-(-4)\pm√((-4)^2-4(2)(-23)))/(2(2))=(4\pm√(200))/(4)=(4\pm√(100\cdot2))/(4)`

`=(4\pm√(100)\cdot\sqrt2)/(4)=(4\pm10\sqrt2)/(4)=1\pm2.5\sqrt2`

Answer 2

My guess is 2+5(square of 2)/ 2 and 2-5(square of 2)/2