Question

Use the quadratic formula to solve the quadratic equation 8x^2+3x=3x−2 . Express its solutions in the form of a±b i

Answer 1

First move all terms to one side: 8x^2+3x−(3x−2)=0 ⇒ 8x^2+2=0.

Here a=8, b=0, c=2. The quadratic formula gives
x = [−b ± sqrt(b^2−4ac)]/(2a) = [0 ± sqrt(0−64)]/16 = ± sqrt(−64)/16 = ± (8i)/16 = ± (1/2)i.

So the solutions are 0 + (1/2)i and 0 − (1/2)i (i.e. x = ± (1/2)i).