4x^2+9x-8100=0

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Solution for 4x^2+9x-8100=0 equation: 


Simplifying
4x2 + 9x + -8100 = 0

Reorder the terms:
-8100 + 9x + 4x2 = 0

Solving
-8100 + 9x + 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'.
-2025 + 2.25x + x2 = 0

Move the constant term to the right:

Add '2025' to each side of the equation.
-2025 + 2.25x + 2025 + x2 = 0 + 2025

Reorder the terms:
-2025 + 2025 + 2.25x + x2 = 0 + 2025

Combine like terms: -2025 + 2025 = 0
0 + 2.25x + x2 = 0 + 2025
2.25x + x2 = 0 + 2025

Combine like terms: 0 + 2025 = 2025
2.25x + x2 = 2025

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 2025 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 2025 + 1.265625

Combine like terms: 2025 + 1.265625 = 2026.265625
1.265625 + 2.25x + x2 = 2026.265625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 2026.265625

Calculate the square root of the right side: 45.014060303

Break this problem into two subproblems by setting 
(x + 1.125) equal to 45.014060303 and -45.014060303.


Subproblem 1
x + 1.125 = 45.014060303

Simplifying
x + 1.125 = 45.014060303

Reorder the terms:
1.125 + x = 45.014060303

Solving
1.125 + x = 45.014060303

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 45.014060303 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 45.014060303 + -1.125
x = 45.014060303 + -1.125

Combine like terms: 45.014060303 + -1.125 = 43.889060303
x = 43.889060303

Simplifying
x = 43.889060303


Subproblem 2
x + 1.125 = -45.014060303

Simplifying
x + 1.125 = -45.014060303

Reorder the terms:
1.125 + x = -45.014060303

Solving
1.125 + x = -45.014060303

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -45.014060303 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -45.014060303 + -1.125
x = -45.014060303 + -1.125

Combine like terms: -45.014060303 + -1.125 = -46.139060303
x = -46.139060303

Simplifying
x = -46.139060303


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43.889060303, -46.139060303}

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