40(x^2+16x-18)=0

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Solution for 40(x^2+16x-18)=0 equation: 


Simplifying
40(x2 + 16x + -18) = 0

Reorder the terms:
40(-18 + 16x + x2) = 0
(-18 * 40 + 16x * 40 + x2 * 40) = 0
(-720 + 640x + 40x2) = 0

Solving
-720 + 640x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '40'.
40(-18 + 16x + x2) = 0

Ignore the factor 40.

Subproblem 1
Set the factor '(-18 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + 16x + x2 = 0

Solving
-18 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 16x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 16x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 16x + x2 = 0 + 18
16x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
16x + x2 = 18

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 18 + 64

Reorder the terms:
64 + 16x + x2 = 18 + 64

Combine like terms: 18 + 64 = 82
64 + 16x + x2 = 82

Factor a perfect square on the left side:
(x + 8)(x + 8) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 8) equal to 9.055385138 and -9.055385138.


Subproblem 1
x + 8 = 9.055385138

Simplifying
x + 8 = 9.055385138

Reorder the terms:
8 + x = 9.055385138

Solving
8 + x = 9.055385138

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 9.055385138 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.055385138 + -8
x = 9.055385138 + -8

Combine like terms: 9.055385138 + -8 = 1.055385138
x = 1.055385138

Simplifying
x = 1.055385138


Subproblem 2
x + 8 = -9.055385138

Simplifying
x + 8 = -9.055385138

Reorder the terms:
8 + x = -9.055385138

Solving
8 + x = -9.055385138

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -9.055385138 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.055385138 + -8
x = -9.055385138 + -8

Combine like terms: -9.055385138 + -8 = -17.055385138
x = -17.055385138

Simplifying
x = -17.055385138


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.055385138, -17.055385138}
Solution
x = {1.055385138, -17.055385138}

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