2x^2+60x-250=0

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Solution for 2x^2+60x-250=0 equation: 


Simplifying
2x2 + 60x + -250 = 0

Reorder the terms:
-250 + 60x + 2x2 = 0

Solving
-250 + 60x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 30x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-125 + 30x + x2 = 0

Solving
-125 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 30x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 30x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 30x + x2 = 0 + 125
30x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
30x + x2 = 125

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 125 + 225

Reorder the terms:
225 + 30x + x2 = 125 + 225

Combine like terms: 125 + 225 = 350
225 + 30x + x2 = 350

Factor a perfect square on the left side:
(x + 15)(x + 15) = 350

Calculate the square root of the right side: 18.708286934

Break this problem into two subproblems by setting 
(x + 15) equal to 18.708286934 and -18.708286934.


Subproblem 1
x + 15 = 18.708286934

Simplifying
x + 15 = 18.708286934

Reorder the terms:
15 + x = 18.708286934

Solving
15 + x = 18.708286934

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 18.708286934 + -15

Combine like terms: 15 + -15 = 0
0 + x = 18.708286934 + -15
x = 18.708286934 + -15

Combine like terms: 18.708286934 + -15 = 3.708286934
x = 3.708286934

Simplifying
x = 3.708286934


Subproblem 2
x + 15 = -18.708286934

Simplifying
x + 15 = -18.708286934

Reorder the terms:
15 + x = -18.708286934

Solving
15 + x = -18.708286934

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -18.708286934 + -15

Combine like terms: 15 + -15 = 0
0 + x = -18.708286934 + -15
x = -18.708286934 + -15

Combine like terms: -18.708286934 + -15 = -33.708286934
x = -33.708286934

Simplifying
x = -33.708286934


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.708286934, -33.708286934}
Solution
x = {3.708286934, -33.708286934}

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