4x*x-10x-390=0

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Solution for 4x*x-10x-390=0 equation: 


Simplifying
4x * x + -10x + -390 = 0

Multiply x * x
4x2 + -10x + -390 = 0

Reorder the terms:
-390 + -10x + 4x2 = 0

Solving
-390 + -10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-195 + -5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-195 + -5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-195 + -5x + 2x2 = 0

Solving
-195 + -5x + 2x2 = 0

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

Divide each side by '2'.
-97.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '97.5' to each side of the equation.
-97.5 + -2.5x + 97.5 + x2 = 0 + 97.5

Reorder the terms:
-97.5 + 97.5 + -2.5x + x2 = 0 + 97.5

Combine like terms: -97.5 + 97.5 = 0.0
0.0 + -2.5x + x2 = 0 + 97.5
-2.5x + x2 = 0 + 97.5

Combine like terms: 0 + 97.5 = 97.5
-2.5x + x2 = 97.5

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 = 97.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 97.5 + 1.5625

Combine like terms: 97.5 + 1.5625 = 99.0625
1.5625 + -2.5x + x2 = 99.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 99.0625

Calculate the square root of the right side: 9.953014619

Break this problem into two subproblems by setting 
(x + -1.25) equal to 9.953014619 and -9.953014619.


Subproblem 1
x + -1.25 = 9.953014619

Simplifying
x + -1.25 = 9.953014619

Reorder the terms:
-1.25 + x = 9.953014619

Solving
-1.25 + x = 9.953014619

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 = 9.953014619 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 9.953014619 + 1.25
x = 9.953014619 + 1.25

Combine like terms: 9.953014619 + 1.25 = 11.203014619
x = 11.203014619

Simplifying
x = 11.203014619


Subproblem 2
x + -1.25 = -9.953014619

Simplifying
x + -1.25 = -9.953014619

Reorder the terms:
-1.25 + x = -9.953014619

Solving
-1.25 + x = -9.953014619

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 = -9.953014619 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -9.953014619 + 1.25
x = -9.953014619 + 1.25

Combine like terms: -9.953014619 + 1.25 = -8.703014619
x = -8.703014619

Simplifying
x = -8.703014619


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.203014619, -8.703014619}
Solution
x = {11.203014619, -8.703014619}

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