Question

solve the equation by using the Quadratic Formula.

−8⁢𝑥^2+4⁢𝑥=−5

Simplify your solutions. If the solutions are real rational numbers, list from least to greatest separated by a comma. If the solutions are not real numbers, write your answer in the form a ± bi. If the solutions are irrational, write your answer in simplified radical form, using ± to express both solutions.

Answer 1

First put in standard form:
-8x^2 + 4x + 5 = 0 => multiply by -1 => 8x^2 - 4x - 5 = 0.

Use the quadratic formula x = [4 ± sqrt((-4)^2 - 4·8·(-5))]/(2·8)
= [4 ± sqrt(16 + 160)]/16
= [4 ± sqrt(176)]/16
= [4 ± 4√11]/16
= (1 ± √11)/4.

From least to greatest: (1 - √11)/4, (1 + √11)/4.