Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 6x = 20

Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x² – 6x = 20

Answer 1

Equation: x² - 6x = 20

Step 1. Multiply the -6 of the x-term by 1/2: -6 * 1/2 = -6/2 = -3

Square the value from step 1: (-3)² = 9, Note: this number will always be positive

Setup the completed square equation. Since (x - 3)² = x² - 6x + 9, you have to add 9 from the right side since it was added when you completed the square.

(x - 3)² = 20 + 9

(x - 3)² = 29

Solve the equation for x. Note: sqrt is shorthand for square root.

square root both sides: x - 3 = ± sqrt(29)

Add 3 to both sides: x = 3 ± sqrt(29)

x = 3 + sqrt(29) ≈ 8.39

x = 3 - sqrt(29) ≈ -2.39

Answers: x ≈ -2.39, 8.39