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