2x^2-124x+600=0

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Solution for 2x^2-124x+600=0 equation: 


Simplifying
2x2 + -124x + 600 = 0

Reorder the terms:
600 + -124x + 2x2 = 0

Solving
600 + -124x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(300 + -62x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(300 + -62x + x2)' equal to zero and attempt to solve:

Simplifying
300 + -62x + x2 = 0

Solving
300 + -62x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-300' to each side of the equation.
300 + -62x + -300 + x2 = 0 + -300

Reorder the terms:
300 + -300 + -62x + x2 = 0 + -300

Combine like terms: 300 + -300 = 0
0 + -62x + x2 = 0 + -300
-62x + x2 = 0 + -300

Combine like terms: 0 + -300 = -300
-62x + x2 = -300

The x term is -62x.  Take half its coefficient (-31).
Square it (961) and add it to both sides.

Add '961' to each side of the equation.
-62x + 961 + x2 = -300 + 961

Reorder the terms:
961 + -62x + x2 = -300 + 961

Combine like terms: -300 + 961 = 661
961 + -62x + x2 = 661

Factor a perfect square on the left side:
(x + -31)(x + -31) = 661

Calculate the square root of the right side: 25.709920264

Break this problem into two subproblems by setting 
(x + -31) equal to 25.709920264 and -25.709920264.


Subproblem 1
x + -31 = 25.709920264

Simplifying
x + -31 = 25.709920264

Reorder the terms:
-31 + x = 25.709920264

Solving
-31 + x = 25.709920264

Solving for variable 'x'.

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

Add '31' to each side of the equation.
-31 + 31 + x = 25.709920264 + 31

Combine like terms: -31 + 31 = 0
0 + x = 25.709920264 + 31
x = 25.709920264 + 31

Combine like terms: 25.709920264 + 31 = 56.709920264
x = 56.709920264

Simplifying
x = 56.709920264


Subproblem 2
x + -31 = -25.709920264

Simplifying
x + -31 = -25.709920264

Reorder the terms:
-31 + x = -25.709920264

Solving
-31 + x = -25.709920264

Solving for variable 'x'.

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

Add '31' to each side of the equation.
-31 + 31 + x = -25.709920264 + 31

Combine like terms: -31 + 31 = 0
0 + x = -25.709920264 + 31
x = -25.709920264 + 31

Combine like terms: -25.709920264 + 31 = 5.290079736
x = 5.290079736

Simplifying
x = 5.290079736


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.709920264, 5.290079736}
Solution
x = {56.709920264, 5.290079736}

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