2(x^2-62x+368)=0

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Solution for 2(x^2-62x+368)=0 equation: 


Simplifying
2(x2 + -62x + 368) = 0

Reorder the terms:
2(368 + -62x + x2) = 0
(368 * 2 + -62x * 2 + x2 * 2) = 0
(736 + -124x + 2x2) = 0

Solving
736 + -124x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(368 + -62x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(368 + -62x + x2)' equal to zero and attempt to solve:

Simplifying
368 + -62x + x2 = 0

Solving
368 + -62x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-368' to each side of the equation.
368 + -62x + -368 + x2 = 0 + -368

Reorder the terms:
368 + -368 + -62x + x2 = 0 + -368

Combine like terms: 368 + -368 = 0
0 + -62x + x2 = 0 + -368
-62x + x2 = 0 + -368

Combine like terms: 0 + -368 = -368
-62x + x2 = -368

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 = -368 + 961

Reorder the terms:
961 + -62x + x2 = -368 + 961

Combine like terms: -368 + 961 = 593
961 + -62x + x2 = 593

Factor a perfect square on the left side:
(x + -31)(x + -31) = 593

Calculate the square root of the right side: 24.351591324

Break this problem into two subproblems by setting 
(x + -31) equal to 24.351591324 and -24.351591324.


Subproblem 1
x + -31 = 24.351591324

Simplifying
x + -31 = 24.351591324

Reorder the terms:
-31 + x = 24.351591324

Solving
-31 + x = 24.351591324

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 = 24.351591324 + 31

Combine like terms: -31 + 31 = 0
0 + x = 24.351591324 + 31
x = 24.351591324 + 31

Combine like terms: 24.351591324 + 31 = 55.351591324
x = 55.351591324

Simplifying
x = 55.351591324


Subproblem 2
x + -31 = -24.351591324

Simplifying
x + -31 = -24.351591324

Reorder the terms:
-31 + x = -24.351591324

Solving
-31 + x = -24.351591324

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 = -24.351591324 + 31

Combine like terms: -31 + 31 = 0
0 + x = -24.351591324 + 31
x = -24.351591324 + 31

Combine like terms: -24.351591324 + 31 = 6.648408676
x = 6.648408676

Simplifying
x = 6.648408676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.351591324, 6.648408676}
Solution
x = {55.351591324, 6.648408676}

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