Answer:
[tex]\large\boxed{1\pm2.5\sqrt2}[/tex]
Step-by-step explanation:
[tex]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=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=2,\ b=-4,\ c=-23\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(-23)}}{2(2)}=\dfrac{4\pm\sqrt{200}}{4}=\dfrac{4\pm\sqrt{100\cdot2}}{4}[/tex]
[tex]=\dfrac{4\pm\sqrt{100}\cdot\sqrt2}{4}=\dfrac{4\pm10\sqrt2}{4}=1\pm2.5\sqrt2[/tex]
