Question

Solve the equation by using the Quadratic Formula.

8⁢𝑥^2−4⁢𝑥+1=0

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

Use the quadratic formula x = [−b ± sqrt(b^2 − 4ac)]/(2a) with a=8, b=−4, c=1:

x = [4 ± sqrt(16 − 32)]/16 = [4 ± sqrt(−16)]/16 = [4 ± 4i]/16 = (1 ± i)/4.

So the solutions are (1/4) ± (1/4)i.