Question

2x^2-4x-18=0
Complete the square

Answer 1

1. Add 18 to both sides to get the -18 term on the right side.

Answer 2

2. You must have x^2 as the first term, so divide both sides by 2.
Do these two steps and show what you got.

Answer 3

Go!

Answer 4

Simplifying
2x2 + 4x + -18 = 0

Reorder the terms:
-18 + 4x + 2x2 = 0

Solving
-18 + 4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 2x + x2 = 0

Solving
-9 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x + x2 = 0 + 9
2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
2x + x2 = 9

The x term is 2x. Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9 + 1

Reorder the terms:
1 + 2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2x + x2 = 10

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting
(x + 1) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 1 = 3.16227766

Simplifying
x + 1 = 3.16227766

Reorder the terms:
1 + x = 3.16227766

Solving
1 + x = 3.16227766

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.16227766 + -1
x = 3.16227766 + -1

Combine like terms: 3.16227766 + -1 = 2.16227766
x = 2.16227766

Simplifying
x = 2.16227766

Subproblem 2
x + 1 = -3.16227766

Simplifying
x + 1 = -3.16227766

Reorder the terms:
1 + x = -3.16227766

Solving
1 + x = -3.16227766

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = -3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.16227766 + -1
x = -3.16227766 + -1

Combine like terms: -3.16227766 + -1 = -4.16227766
x = -4.16227766

Simplifying
x = -4.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.16227766, -4.16227766}
Solution
x = {2.16227766, -4.16227766}