2x^2+100x-600=0

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Solution for 2x^2+100x-600=0 equation: 


Simplifying
2x2 + 100x + -600 = 0

Reorder the terms:
-600 + 100x + 2x2 = 0

Solving
-600 + 100x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-300 + 50x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-300 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
-300 + 50x + x2 = 0

Solving
-300 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 50x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 50x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 50x + x2 = 0 + 300
50x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
50x + x2 = 300

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 300 + 625

Reorder the terms:
625 + 50x + x2 = 300 + 625

Combine like terms: 300 + 625 = 925
625 + 50x + x2 = 925

Factor a perfect square on the left side:
(x + 25)(x + 25) = 925

Calculate the square root of the right side: 30.413812651

Break this problem into two subproblems by setting 
(x + 25) equal to 30.413812651 and -30.413812651.


Subproblem 1
x + 25 = 30.413812651

Simplifying
x + 25 = 30.413812651

Reorder the terms:
25 + x = 30.413812651

Solving
25 + x = 30.413812651

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 30.413812651 + -25

Combine like terms: 25 + -25 = 0
0 + x = 30.413812651 + -25
x = 30.413812651 + -25

Combine like terms: 30.413812651 + -25 = 5.413812651
x = 5.413812651

Simplifying
x = 5.413812651


Subproblem 2
x + 25 = -30.413812651

Simplifying
x + 25 = -30.413812651

Reorder the terms:
25 + x = -30.413812651

Solving
25 + x = -30.413812651

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -30.413812651 + -25

Combine like terms: 25 + -25 = 0
0 + x = -30.413812651 + -25
x = -30.413812651 + -25

Combine like terms: -30.413812651 + -25 = -55.413812651
x = -55.413812651

Simplifying
x = -55.413812651


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.413812651, -55.413812651}
Solution
x = {5.413812651, -55.413812651}

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