2(4x^2-10x-325)=0

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Solution for 2(4x^2-10x-325)=0 equation: 


Simplifying
2(4x2 + -10x + -325) = 0

Reorder the terms:
2(-325 + -10x + 4x2) = 0
(-325 * 2 + -10x * 2 + 4x2 * 2) = 0
(-650 + -20x + 8x2) = 0

Solving
-650 + -20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-325 + -10x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-325 + -10x + 4x2)' equal to zero and attempt to solve:

Simplifying
-325 + -10x + 4x2 = 0

Solving
-325 + -10x + 4x2 = 0

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

Divide each side by '4'.
-81.25 + -2.5x + x2 = 0

Move the constant term to the right:

Add '81.25' to each side of the equation.
-81.25 + -2.5x + 81.25 + x2 = 0 + 81.25

Reorder the terms:
-81.25 + 81.25 + -2.5x + x2 = 0 + 81.25

Combine like terms: -81.25 + 81.25 = 0.00
0.00 + -2.5x + x2 = 0 + 81.25
-2.5x + x2 = 0 + 81.25

Combine like terms: 0 + 81.25 = 81.25
-2.5x + x2 = 81.25

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 81.25 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 81.25 + 1.5625

Combine like terms: 81.25 + 1.5625 = 82.8125
1.5625 + -2.5x + x2 = 82.8125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 82.8125

Calculate the square root of the right side: 9.100137362

Break this problem into two subproblems by setting 
(x + -1.25) equal to 9.100137362 and -9.100137362.


Subproblem 1
x + -1.25 = 9.100137362

Simplifying
x + -1.25 = 9.100137362

Reorder the terms:
-1.25 + x = 9.100137362

Solving
-1.25 + x = 9.100137362

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 9.100137362 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 9.100137362 + 1.25
x = 9.100137362 + 1.25

Combine like terms: 9.100137362 + 1.25 = 10.350137362
x = 10.350137362

Simplifying
x = 10.350137362


Subproblem 2
x + -1.25 = -9.100137362

Simplifying
x + -1.25 = -9.100137362

Reorder the terms:
-1.25 + x = -9.100137362

Solving
-1.25 + x = -9.100137362

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -9.100137362 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -9.100137362 + 1.25
x = -9.100137362 + 1.25

Combine like terms: -9.100137362 + 1.25 = -7.850137362
x = -7.850137362

Simplifying
x = -7.850137362


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.350137362, -7.850137362}
Solution
x = {10.350137362, -7.850137362}

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