2x^2-10x-150=0

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Solution for 2x^2-10x-150=0 equation: 


Simplifying
2x2 + -10x + -150 = 0

Reorder the terms:
-150 + -10x + 2x2 = 0

Solving
-150 + -10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-75 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + -5x + x2 = 0

Solving
-75 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -5x + x2 = 0 + 75
-5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-5x + x2 = 75

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 = 75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 75 + 6.25

Combine like terms: 75 + 6.25 = 81.25
6.25 + -5x + x2 = 81.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(x + -2.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
x + -2.5 = 9.013878189

Simplifying
x + -2.5 = 9.013878189

Reorder the terms:
-2.5 + x = 9.013878189

Solving
-2.5 + x = 9.013878189

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 = 9.013878189 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 9.013878189 + 2.5
x = 9.013878189 + 2.5

Combine like terms: 9.013878189 + 2.5 = 11.513878189
x = 11.513878189

Simplifying
x = 11.513878189


Subproblem 2
x + -2.5 = -9.013878189

Simplifying
x + -2.5 = -9.013878189

Reorder the terms:
-2.5 + x = -9.013878189

Solving
-2.5 + x = -9.013878189

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 = -9.013878189 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -9.013878189 + 2.5
x = -9.013878189 + 2.5

Combine like terms: -9.013878189 + 2.5 = -6.513878189
x = -6.513878189

Simplifying
x = -6.513878189


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.513878189, -6.513878189}
Solution
x = {11.513878189, -6.513878189}

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