4x^2+4x-36=36

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Solution for 4x^2+4x-36=36 equation: 


Simplifying
4x2 + 4x + -36 = 36

Reorder the terms:
-36 + 4x + 4x2 = 36

Solving
-36 + 4x + 4x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + -36 + 4x + 4x2 = 36 + -36

Combine like terms: -36 + -36 = -72
-72 + 4x + 4x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-72 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + x + x2) = 0

Ignore the factor 4.

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

Simplifying
-18 + x + x2 = 0

Solving
-18 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 18 + 0.25

Reorder the terms:
0.25 + x + x2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + x + x2 = 18.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 0.5 = 4.272001873

Simplifying
x + 0.5 = 4.272001873

Reorder the terms:
0.5 + x = 4.272001873

Solving
0.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.272001873 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.272001873 + -0.5
x = 4.272001873 + -0.5

Combine like terms: 4.272001873 + -0.5 = 3.772001873
x = 3.772001873

Simplifying
x = 3.772001873


Subproblem 2
x + 0.5 = -4.272001873

Simplifying
x + 0.5 = -4.272001873

Reorder the terms:
0.5 + x = -4.272001873

Solving
0.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.272001873 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.272001873 + -0.5
x = -4.272001873 + -0.5

Combine like terms: -4.272001873 + -0.5 = -4.772001873
x = -4.772001873

Simplifying
x = -4.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.772001873, -4.772001873}
Solution
x = {3.772001873, -4.772001873}

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