4(x^2+22x-159)=0

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Solution for 4(x^2+22x-159)=0 equation: 


Simplifying
4(x2 + 22x + -159) = 0

Reorder the terms:
4(-159 + 22x + x2) = 0
(-159 * 4 + 22x * 4 + x2 * 4) = 0
(-636 + 88x + 4x2) = 0

Solving
-636 + 88x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-159 + 22x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-159 + 22x + x2)' equal to zero and attempt to solve:

Simplifying
-159 + 22x + x2 = 0

Solving
-159 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '159' to each side of the equation.
-159 + 22x + 159 + x2 = 0 + 159

Reorder the terms:
-159 + 159 + 22x + x2 = 0 + 159

Combine like terms: -159 + 159 = 0
0 + 22x + x2 = 0 + 159
22x + x2 = 0 + 159

Combine like terms: 0 + 159 = 159
22x + x2 = 159

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 159 + 121

Reorder the terms:
121 + 22x + x2 = 159 + 121

Combine like terms: 159 + 121 = 280
121 + 22x + x2 = 280

Factor a perfect square on the left side:
(x + 11)(x + 11) = 280

Calculate the square root of the right side: 16.733200531

Break this problem into two subproblems by setting 
(x + 11) equal to 16.733200531 and -16.733200531.


Subproblem 1
x + 11 = 16.733200531

Simplifying
x + 11 = 16.733200531

Reorder the terms:
11 + x = 16.733200531

Solving
11 + x = 16.733200531

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 16.733200531 + -11

Combine like terms: 11 + -11 = 0
0 + x = 16.733200531 + -11
x = 16.733200531 + -11

Combine like terms: 16.733200531 + -11 = 5.733200531
x = 5.733200531

Simplifying
x = 5.733200531


Subproblem 2
x + 11 = -16.733200531

Simplifying
x + 11 = -16.733200531

Reorder the terms:
11 + x = -16.733200531

Solving
11 + x = -16.733200531

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -16.733200531 + -11

Combine like terms: 11 + -11 = 0
0 + x = -16.733200531 + -11
x = -16.733200531 + -11

Combine like terms: -16.733200531 + -11 = -27.733200531
x = -27.733200531

Simplifying
x = -27.733200531


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.733200531, -27.733200531}
Solution
x = {5.733200531, -27.733200531}

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