2x^2+50x-600=0

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Solution for 2x^2+50x-600=0 equation: 


Simplifying
2x2 + 50x + -600 = 0

Reorder the terms:
-600 + 50x + 2x2 = 0

Solving
-600 + 50x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-300 + 25x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-300 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-300 + 25x + x2 = 0

Solving
-300 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 25x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 25x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 25x + x2 = 0 + 300
25x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
25x + x2 = 300

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 300 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 300 + 156.25

Combine like terms: 300 + 156.25 = 456.25
156.25 + 25x + x2 = 456.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 456.25

Calculate the square root of the right side: 21.360009363

Break this problem into two subproblems by setting 
(x + 12.5) equal to 21.360009363 and -21.360009363.


Subproblem 1
x + 12.5 = 21.360009363

Simplifying
x + 12.5 = 21.360009363

Reorder the terms:
12.5 + x = 21.360009363

Solving
12.5 + x = 21.360009363

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 21.360009363 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 21.360009363 + -12.5
x = 21.360009363 + -12.5

Combine like terms: 21.360009363 + -12.5 = 8.860009363
x = 8.860009363

Simplifying
x = 8.860009363


Subproblem 2
x + 12.5 = -21.360009363

Simplifying
x + 12.5 = -21.360009363

Reorder the terms:
12.5 + x = -21.360009363

Solving
12.5 + x = -21.360009363

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -21.360009363 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -21.360009363 + -12.5
x = -21.360009363 + -12.5

Combine like terms: -21.360009363 + -12.5 = -33.860009363
x = -33.860009363

Simplifying
x = -33.860009363


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.860009363, -33.860009363}
Solution
x = {8.860009363, -33.860009363}

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