x^2-59x+216=0

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Solution for x^2-59x+216=0 equation: 


Simplifying
x2 + -59x + 216 = 0

Reorder the terms:
216 + -59x + x2 = 0

Solving
216 + -59x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-216' to each side of the equation.
216 + -59x + -216 + x2 = 0 + -216

Reorder the terms:
216 + -216 + -59x + x2 = 0 + -216

Combine like terms: 216 + -216 = 0
0 + -59x + x2 = 0 + -216
-59x + x2 = 0 + -216

Combine like terms: 0 + -216 = -216
-59x + x2 = -216

The x term is -59x.  Take half its coefficient (-29.5).
Square it (870.25) and add it to both sides.

Add '870.25' to each side of the equation.
-59x + 870.25 + x2 = -216 + 870.25

Reorder the terms:
870.25 + -59x + x2 = -216 + 870.25

Combine like terms: -216 + 870.25 = 654.25
870.25 + -59x + x2 = 654.25

Factor a perfect square on the left side:
(x + -29.5)(x + -29.5) = 654.25

Calculate the square root of the right side: 25.578311125

Break this problem into two subproblems by setting 
(x + -29.5) equal to 25.578311125 and -25.578311125.


Subproblem 1
x + -29.5 = 25.578311125

Simplifying
x + -29.5 = 25.578311125

Reorder the terms:
-29.5 + x = 25.578311125

Solving
-29.5 + x = 25.578311125

Solving for variable 'x'.

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

Add '29.5' to each side of the equation.
-29.5 + 29.5 + x = 25.578311125 + 29.5

Combine like terms: -29.5 + 29.5 = 0.0
0.0 + x = 25.578311125 + 29.5
x = 25.578311125 + 29.5

Combine like terms: 25.578311125 + 29.5 = 55.078311125
x = 55.078311125

Simplifying
x = 55.078311125


Subproblem 2
x + -29.5 = -25.578311125

Simplifying
x + -29.5 = -25.578311125

Reorder the terms:
-29.5 + x = -25.578311125

Solving
-29.5 + x = -25.578311125

Solving for variable 'x'.

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

Add '29.5' to each side of the equation.
-29.5 + 29.5 + x = -25.578311125 + 29.5

Combine like terms: -29.5 + 29.5 = 0.0
0.0 + x = -25.578311125 + 29.5
x = -25.578311125 + 29.5

Combine like terms: -25.578311125 + 29.5 = 3.921688875
x = 3.921688875

Simplifying
x = 3.921688875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.078311125, 3.921688875}

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