4x^2+58x-1014=0

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Solution for 4x^2+58x-1014=0 equation: 


Simplifying
4x2 + 58x + -1014 = 0

Reorder the terms:
-1014 + 58x + 4x2 = 0

Solving
-1014 + 58x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-507 + 29x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-507 + 29x + 2x2)' equal to zero and attempt to solve:

Simplifying
-507 + 29x + 2x2 = 0

Solving
-507 + 29x + 2x2 = 0

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

Divide each side by '2'.
-253.5 + 14.5x + x2 = 0

Move the constant term to the right:

Add '253.5' to each side of the equation.
-253.5 + 14.5x + 253.5 + x2 = 0 + 253.5

Reorder the terms:
-253.5 + 253.5 + 14.5x + x2 = 0 + 253.5

Combine like terms: -253.5 + 253.5 = 0.0
0.0 + 14.5x + x2 = 0 + 253.5
14.5x + x2 = 0 + 253.5

Combine like terms: 0 + 253.5 = 253.5
14.5x + x2 = 253.5

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = 253.5 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = 253.5 + 52.5625

Combine like terms: 253.5 + 52.5625 = 306.0625
52.5625 + 14.5x + x2 = 306.0625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 306.0625

Calculate the square root of the right side: 17.494642037

Break this problem into two subproblems by setting 
(x + 7.25) equal to 17.494642037 and -17.494642037.


Subproblem 1
x + 7.25 = 17.494642037

Simplifying
x + 7.25 = 17.494642037

Reorder the terms:
7.25 + x = 17.494642037

Solving
7.25 + x = 17.494642037

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = 17.494642037 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = 17.494642037 + -7.25
x = 17.494642037 + -7.25

Combine like terms: 17.494642037 + -7.25 = 10.244642037
x = 10.244642037

Simplifying
x = 10.244642037


Subproblem 2
x + 7.25 = -17.494642037

Simplifying
x + 7.25 = -17.494642037

Reorder the terms:
7.25 + x = -17.494642037

Solving
7.25 + x = -17.494642037

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = -17.494642037 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = -17.494642037 + -7.25
x = -17.494642037 + -7.25

Combine like terms: -17.494642037 + -7.25 = -24.744642037
x = -24.744642037

Simplifying
x = -24.744642037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.244642037, -24.744642037}
Solution
x = {10.244642037, -24.744642037}

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