PSAT Math Multiple-Choice Question 583: Answer and Explanation

Question: 583

What are the two solutions for x in the equation 4x² + 8x - 4 = 0

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

(D) Solve by simplifying and completing the square:

4x² + 8x - 4 = 0

x² + 2x - 1 = 0

x² + 2x = 1

Then complete the square by adding 1 to both sides:

x² + 2x + 1 = 2

Then factor the left-hand side:

(x + 1)² = 2

Then take the square root of both sides, remembering to include both the positive and the negative values on the right:

x + 1 = and x + 1 = -

Solve for x to find the solutions:

and

Alternatively, you could solve this using the quadratic equation. Start by dividing by 4 to
simplify:

4x² + 8x - 4 = 0

x² + 2x - 1 = 0

This is equivalent to the answers and .