4x^2+378x-13631=0

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Solution for 4x^2+378x-13631=0 equation: 


Simplifying
4x2 + 378x + -13631 = 0

Reorder the terms:
-13631 + 378x + 4x2 = 0

Solving
-13631 + 378x + 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'.
-3407.75 + 94.5x + x2 = 0

Move the constant term to the right:

Add '3407.75' to each side of the equation.
-3407.75 + 94.5x + 3407.75 + x2 = 0 + 3407.75

Reorder the terms:
-3407.75 + 3407.75 + 94.5x + x2 = 0 + 3407.75

Combine like terms: -3407.75 + 3407.75 = 0.00
0.00 + 94.5x + x2 = 0 + 3407.75
94.5x + x2 = 0 + 3407.75

Combine like terms: 0 + 3407.75 = 3407.75
94.5x + x2 = 3407.75

The x term is 94.5x.  Take half its coefficient (47.25).
Square it (2232.5625) and add it to both sides.

Add '2232.5625' to each side of the equation.
94.5x + 2232.5625 + x2 = 3407.75 + 2232.5625

Reorder the terms:
2232.5625 + 94.5x + x2 = 3407.75 + 2232.5625

Combine like terms: 3407.75 + 2232.5625 = 5640.3125
2232.5625 + 94.5x + x2 = 5640.3125

Factor a perfect square on the left side:
(x + 47.25)(x + 47.25) = 5640.3125

Calculate the square root of the right side: 75.102013954

Break this problem into two subproblems by setting 
(x + 47.25) equal to 75.102013954 and -75.102013954.


Subproblem 1
x + 47.25 = 75.102013954

Simplifying
x + 47.25 = 75.102013954

Reorder the terms:
47.25 + x = 75.102013954

Solving
47.25 + x = 75.102013954

Solving for variable 'x'.

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

Add '-47.25' to each side of the equation.
47.25 + -47.25 + x = 75.102013954 + -47.25

Combine like terms: 47.25 + -47.25 = 0.00
0.00 + x = 75.102013954 + -47.25
x = 75.102013954 + -47.25

Combine like terms: 75.102013954 + -47.25 = 27.852013954
x = 27.852013954

Simplifying
x = 27.852013954


Subproblem 2
x + 47.25 = -75.102013954

Simplifying
x + 47.25 = -75.102013954

Reorder the terms:
47.25 + x = -75.102013954

Solving
47.25 + x = -75.102013954

Solving for variable 'x'.

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

Add '-47.25' to each side of the equation.
47.25 + -47.25 + x = -75.102013954 + -47.25

Combine like terms: 47.25 + -47.25 = 0.00
0.00 + x = -75.102013954 + -47.25
x = -75.102013954 + -47.25

Combine like terms: -75.102013954 + -47.25 = -122.352013954
x = -122.352013954

Simplifying
x = -122.352013954


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.852013954, -122.352013954}

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