4x^2+36x-81=0

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Solution for 4x^2+36x-81=0 equation:


Simplifying
4x2 + 36x + -81 = 0

Reorder the terms:
-81 + 36x + 4x2 = 0

Solving
-81 + 36x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-20.25 + 9x + x2 = 0

Move the constant term to the right:

Add '20.25' to each side of the equation.
-20.25 + 9x + 20.25 + x2 = 0 + 20.25

Reorder the terms:
-20.25 + 20.25 + 9x + x2 = 0 + 20.25

Combine like terms: -20.25 + 20.25 = 0.00
0.00 + 9x + x2 = 0 + 20.25
9x + x2 = 0 + 20.25

Combine like terms: 0 + 20.25 = 20.25
9x + x2 = 20.25

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 = 20.25 + 20.25

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

Combine like terms: 20.25 + 20.25 = 40.5
20.25 + 9x + x2 = 40.5

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 40.5

Calculate the square root of the right side: 6.363961031

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.363961031 and -6.363961031.


Subproblem 1
x + 4.5 = 6.363961031

Simplifying
x + 4.5 = 6.363961031

Reorder the terms:
4.5 + x = 6.363961031

Solving
4.5 + x = 6.363961031

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 = 6.363961031 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.363961031 + -4.5
x = 6.363961031 + -4.5

Combine like terms: 6.363961031 + -4.5 = 1.863961031
x = 1.863961031

Simplifying
x = 1.863961031


Subproblem 2
x + 4.5 = -6.363961031

Simplifying
x + 4.5 = -6.363961031

Reorder the terms:
4.5 + x = -6.363961031

Solving
4.5 + x = -6.363961031

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 = -6.363961031 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.363961031 + -4.5
x = -6.363961031 + -4.5

Combine like terms: -6.363961031 + -4.5 = -10.863961031
x = -10.863961031

Simplifying
x = -10.863961031


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.863961031, -10.863961031}

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