Question

Find the exact solutions to 2x2 = 5x – 1 by using the quadratic formula.

Answer 1

(1) Collect all terms on one side ⇒ ax² + bx + c = 0 do it so "ax²" is positive
2x² - 5x + 1 = 0 ←only need to change sign of moved terms
(2) Identify a, b, and c ⇒ a = 2, b = -5, and c = 1
(3) Substitute values into the quadratic formula:
`x= \frac{-b+/- \sqrt{ b^(2)-4ac} }{2a}`

`x= \frac{-(-5)+/- \sqrt{ (-5)^(2)-4(2)(1)} }{2(2)}`

`x_(1) = (5+ √(17) )/(4)`

`x_(2) = (5- √(17) )/(4)`