Solve by completing the square. Write your answer in exact form. x² = 5x + 2

Question

Quizplus · Accepted Answer

Start by moving the constant term to the right side:

x^2 + 5x = -2

Next, divide the coefficient of x by 2, square the result, and add/subtract it to both sides of the equation:

x^2 + 5x + (5/2)^2 = -2 + (5/2)^2 
(x + 5/2)^2 = -9/4

Finally, take the square root of both sides, remembering to include the ±:

x + 5/2 = ±(3i/2) 
x = -5/2 ± (3i/2)

The exact form of the solutions is x = -5/2 ± (3i/2), which matches choice C.

Solve by Completing the Square