Question

When completing the square, what factor must be added to the quadratic equation 2x2 + 3x – 3 = 0 to solve it?

Answer 1

x = sqrt(33)/4 - 3/4 or x = -3/4 - sqrt(33)/4

Explanation:

Solve for x over the real numbers:

2 x^2 + 3 x - 3 = 0

Divide both sides by 2:

x^2 + (3 x)/2 - 3/2 = 0

Add 3/2 to both sides:

x^2 + (3 x)/2 = 3/2

Add 9/16 to both sides:

x^2 + (3 x)/2 + 9/16 = 33/16

Write the left hand side as a square:

(x + 3/4)^2 = 33/16

Take the square root of both sides:

x + 3/4 = sqrt(33)/4 or x + 3/4 = -sqrt(33)/4

Subtract 3/4 from both sides:

x = sqrt(33)/4 - 3/4 or x + 3/4 = -sqrt(33)/4

Subtract 3/4 from both sides:

Answer: x = sqrt(33)/4 - 3/4 or x = -3/4 - sqrt(33)/4