x^2+51x-236=0

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Solution for x^2+51x-236=0 equation: 


Simplifying
x2 + 51x + -236 = 0

Reorder the terms:
-236 + 51x + x2 = 0

Solving
-236 + 51x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '236' to each side of the equation.
-236 + 51x + 236 + x2 = 0 + 236

Reorder the terms:
-236 + 236 + 51x + x2 = 0 + 236

Combine like terms: -236 + 236 = 0
0 + 51x + x2 = 0 + 236
51x + x2 = 0 + 236

Combine like terms: 0 + 236 = 236
51x + x2 = 236

The x term is 51x.  Take half its coefficient (25.5).
Square it (650.25) and add it to both sides.

Add '650.25' to each side of the equation.
51x + 650.25 + x2 = 236 + 650.25

Reorder the terms:
650.25 + 51x + x2 = 236 + 650.25

Combine like terms: 236 + 650.25 = 886.25
650.25 + 51x + x2 = 886.25

Factor a perfect square on the left side:
(x + 25.5)(x + 25.5) = 886.25

Calculate the square root of the right side: 29.769951293

Break this problem into two subproblems by setting 
(x + 25.5) equal to 29.769951293 and -29.769951293.


Subproblem 1
x + 25.5 = 29.769951293

Simplifying
x + 25.5 = 29.769951293

Reorder the terms:
25.5 + x = 29.769951293

Solving
25.5 + x = 29.769951293

Solving for variable 'x'.

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

Add '-25.5' to each side of the equation.
25.5 + -25.5 + x = 29.769951293 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + x = 29.769951293 + -25.5
x = 29.769951293 + -25.5

Combine like terms: 29.769951293 + -25.5 = 4.269951293
x = 4.269951293

Simplifying
x = 4.269951293


Subproblem 2
x + 25.5 = -29.769951293

Simplifying
x + 25.5 = -29.769951293

Reorder the terms:
25.5 + x = -29.769951293

Solving
25.5 + x = -29.769951293

Solving for variable 'x'.

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

Add '-25.5' to each side of the equation.
25.5 + -25.5 + x = -29.769951293 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + x = -29.769951293 + -25.5
x = -29.769951293 + -25.5

Combine like terms: -29.769951293 + -25.5 = -55.269951293
x = -55.269951293

Simplifying
x = -55.269951293


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.269951293, -55.269951293}

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