2x^2-10x-750=0

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Solution for 2x^2-10x-750=0 equation: 


Simplifying
2x2 + -10x + -750 = 0

Reorder the terms:
-750 + -10x + 2x2 = 0

Solving
-750 + -10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-375 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-375 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-375 + -5x + x2 = 0

Solving
-375 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '375' to each side of the equation.
-375 + -5x + 375 + x2 = 0 + 375

Reorder the terms:
-375 + 375 + -5x + x2 = 0 + 375

Combine like terms: -375 + 375 = 0
0 + -5x + x2 = 0 + 375
-5x + x2 = 0 + 375

Combine like terms: 0 + 375 = 375
-5x + x2 = 375

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 375 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 375 + 6.25

Combine like terms: 375 + 6.25 = 381.25
6.25 + -5x + x2 = 381.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 381.25

Calculate the square root of the right side: 19.52562419

Break this problem into two subproblems by setting 
(x + -2.5) equal to 19.52562419 and -19.52562419.


Subproblem 1
x + -2.5 = 19.52562419

Simplifying
x + -2.5 = 19.52562419

Reorder the terms:
-2.5 + x = 19.52562419

Solving
-2.5 + x = 19.52562419

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 19.52562419 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 19.52562419 + 2.5
x = 19.52562419 + 2.5

Combine like terms: 19.52562419 + 2.5 = 22.02562419
x = 22.02562419

Simplifying
x = 22.02562419


Subproblem 2
x + -2.5 = -19.52562419

Simplifying
x + -2.5 = -19.52562419

Reorder the terms:
-2.5 + x = -19.52562419

Solving
-2.5 + x = -19.52562419

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -19.52562419 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -19.52562419 + 2.5
x = -19.52562419 + 2.5

Combine like terms: -19.52562419 + 2.5 = -17.02562419
x = -17.02562419

Simplifying
x = -17.02562419


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.02562419, -17.02562419}
Solution
x = {22.02562419, -17.02562419}

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