Question

Solve for 2x^2-4x+5=6

Answer 1

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 = $\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$   Plug in your values
x = $\frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-1)} }{2(2)}$   Simplify
x = $\frac{4 \pm \sqrt{16 + 8} }{4}$   Simplify
x = $\frac{4 \pm 2\sqrt{6} }{4}$   Simplify by removing a 2 from every term
x = $\frac{2 \pm \sqrt{6} }{2}$   Simplify by taking the fraction apart
x = $\frac{2}{2} \pm \frac{ \sqrt{6} }{2}$   Change $\frac{2}{2}$ to 1
x = 1 $\pm \frac{ \sqrt{6} }{2}$   Simplify $\frac{ \sqrt{6} }{2}$ to $\sqrt{ \frac{3}{2} }$
x = 1 $\pm \sqrt{ \frac{3}{2} }$