4x^2+36x-84=0

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Solution for 4x^2+36x-84=0 equation: 


Simplifying
4x2 + 36x + -84 = 0

Reorder the terms:
-84 + 36x + 4x2 = 0

Solving
-84 + 36x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-21 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + 9x + x2 = 0

Solving
-21 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 9x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 9x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 9x + x2 = 0 + 21
9x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
9x + x2 = 21

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 21 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 21 + 20.25

Combine like terms: 21 + 20.25 = 41.25
20.25 + 9x + x2 = 41.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + 4.5 = 6.422616289

Simplifying
x + 4.5 = 6.422616289

Reorder the terms:
4.5 + x = 6.422616289

Solving
4.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 6.422616289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.422616289 + -4.5
x = 6.422616289 + -4.5

Combine like terms: 6.422616289 + -4.5 = 1.922616289
x = 1.922616289

Simplifying
x = 1.922616289


Subproblem 2
x + 4.5 = -6.422616289

Simplifying
x + 4.5 = -6.422616289

Reorder the terms:
4.5 + x = -6.422616289

Solving
4.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -6.422616289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.422616289 + -4.5
x = -6.422616289 + -4.5

Combine like terms: -6.422616289 + -4.5 = -10.922616289
x = -10.922616289

Simplifying
x = -10.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.922616289, -10.922616289}
Solution
x = {1.922616289, -10.922616289}

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