4x^2-484x-3630=0

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Solution for 4x^2-484x-3630=0 equation: 


Simplifying
4x2 + -484x + -3630 = 0

Reorder the terms:
-3630 + -484x + 4x2 = 0

Solving
-3630 + -484x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1815 + -242x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1815 + -242x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1815 + -242x + 2x2 = 0

Solving
-1815 + -242x + 2x2 = 0

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

Divide each side by '2'.
-907.5 + -121x + x2 = 0

Move the constant term to the right:

Add '907.5' to each side of the equation.
-907.5 + -121x + 907.5 + x2 = 0 + 907.5

Reorder the terms:
-907.5 + 907.5 + -121x + x2 = 0 + 907.5

Combine like terms: -907.5 + 907.5 = 0.0
0.0 + -121x + x2 = 0 + 907.5
-121x + x2 = 0 + 907.5

Combine like terms: 0 + 907.5 = 907.5
-121x + x2 = 907.5

The x term is -121x.  Take half its coefficient (-60.5).
Square it (3660.25) and add it to both sides.

Add '3660.25' to each side of the equation.
-121x + 3660.25 + x2 = 907.5 + 3660.25

Reorder the terms:
3660.25 + -121x + x2 = 907.5 + 3660.25

Combine like terms: 907.5 + 3660.25 = 4567.75
3660.25 + -121x + x2 = 4567.75

Factor a perfect square on the left side:
(x + -60.5)(x + -60.5) = 4567.75

Calculate the square root of the right side: 67.585131501

Break this problem into two subproblems by setting 
(x + -60.5) equal to 67.585131501 and -67.585131501.


Subproblem 1
x + -60.5 = 67.585131501

Simplifying
x + -60.5 = 67.585131501

Reorder the terms:
-60.5 + x = 67.585131501

Solving
-60.5 + x = 67.585131501

Solving for variable 'x'.

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

Add '60.5' to each side of the equation.
-60.5 + 60.5 + x = 67.585131501 + 60.5

Combine like terms: -60.5 + 60.5 = 0.0
0.0 + x = 67.585131501 + 60.5
x = 67.585131501 + 60.5

Combine like terms: 67.585131501 + 60.5 = 128.085131501
x = 128.085131501

Simplifying
x = 128.085131501


Subproblem 2
x + -60.5 = -67.585131501

Simplifying
x + -60.5 = -67.585131501

Reorder the terms:
-60.5 + x = -67.585131501

Solving
-60.5 + x = -67.585131501

Solving for variable 'x'.

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

Add '60.5' to each side of the equation.
-60.5 + 60.5 + x = -67.585131501 + 60.5

Combine like terms: -60.5 + 60.5 = 0.0
0.0 + x = -67.585131501 + 60.5
x = -67.585131501 + 60.5

Combine like terms: -67.585131501 + 60.5 = -7.085131501
x = -7.085131501

Simplifying
x = -7.085131501


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {128.085131501, -7.085131501}
Solution
x = {128.085131501, -7.085131501}

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