Quadratic equation by completing the square

Question

Solve the quadratic equation by completing the square. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

x² + 6x + 6 = 0

Answer 1

x² + 6x + 6 = 0

Step 1: Subtract 6 from both sides:

x² + 6x + = -6

Step 2: Find the number that allows you to write the left side of the equation as a square. To find that number take 1/2 of the value in front of the "x" (6/2 = 3) and square it (3² = 9). So add 9 to both sides of the equation:

x² + 6x + 9 = -6 + 9

Step 3: Write the left side of the equation as a square. To do that, group with the "x" the number you got when you took 1/2 of the value in front of the "x". Since that was "3", the square will be (x + 3)². Also, simplify the right side of the equation:

(x + 3)² = 3

Step 4: Take the square root of both sides of the equation. Remember that there are both plus and minus values when you take the square root:

x + 3 = ±√3

Step 5: Subtract 3 from both sides:

x = -3 ± √3

So the answers are x = -3 + √3 and x = -3 - √3