To solve for a variable, you need to get it (x) by itself.
2x² - 4x + 5 = 6 Subtract 6 from both sides
2x² - 4x - 1 = 0 Plug this into the Quadratic Formula
a = 2 , b = -4 , c = -1
x = [tex] \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} [/tex] Plug in your values
x = [tex] \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-1)} }{2(2)} [/tex] Simplify
x = [tex] \frac{4 \pm \sqrt{16 + 8} }{4} [/tex] Simplify
x = [tex]\frac{4 \pm 2\sqrt{6} }{4}[/tex] Simplify by removing a 2 from every term
x = [tex]\frac{2 \pm \sqrt{6} }{2}[/tex] Simplify by taking the fraction apart
x = [tex] \frac{2}{2} \pm \frac{ \sqrt{6} }{2} [/tex] Change [tex] \frac{2}{2} [/tex] to 1
x = 1 [tex]\pm \frac{ \sqrt{6} }{2} [/tex] Simplify [tex] \frac{ \sqrt{6} }{2} [/tex] to [tex] \sqrt{ \frac{3}{2} } [/tex]
x = 1 [tex]\pm \sqrt{ \frac{3}{2} }[/tex]
