2x^2+42x-250=0

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Solution for 2x^2+42x-250=0 equation: 


Simplifying
2x2 + 42x + -250 = 0

Reorder the terms:
-250 + 42x + 2x2 = 0

Solving
-250 + 42x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 21x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
-125 + 21x + x2 = 0

Solving
-125 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 21x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 21x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 21x + x2 = 0 + 125
21x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
21x + x2 = 125

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 125 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 125 + 110.25

Combine like terms: 125 + 110.25 = 235.25
110.25 + 21x + x2 = 235.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 235.25

Calculate the square root of the right side: 15.33786165

Break this problem into two subproblems by setting 
(x + 10.5) equal to 15.33786165 and -15.33786165.


Subproblem 1
x + 10.5 = 15.33786165

Simplifying
x + 10.5 = 15.33786165

Reorder the terms:
10.5 + x = 15.33786165

Solving
10.5 + x = 15.33786165

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 15.33786165 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 15.33786165 + -10.5
x = 15.33786165 + -10.5

Combine like terms: 15.33786165 + -10.5 = 4.83786165
x = 4.83786165

Simplifying
x = 4.83786165


Subproblem 2
x + 10.5 = -15.33786165

Simplifying
x + 10.5 = -15.33786165

Reorder the terms:
10.5 + x = -15.33786165

Solving
10.5 + x = -15.33786165

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -15.33786165 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -15.33786165 + -10.5
x = -15.33786165 + -10.5

Combine like terms: -15.33786165 + -10.5 = -25.83786165
x = -25.83786165

Simplifying
x = -25.83786165


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.83786165, -25.83786165}
Solution
x = {4.83786165, -25.83786165}

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