x^2-10x-51=0

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Solution for x^2-10x-51=0 equation: 


Simplifying
x2 + -10x + -51 = 0

Reorder the terms:
-51 + -10x + x2 = 0

Solving
-51 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -10x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -10x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -10x + x2 = 0 + 51
-10x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-10x + x2 = 51

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 51 + 25

Reorder the terms:
25 + -10x + x2 = 51 + 25

Combine like terms: 51 + 25 = 76
25 + -10x + x2 = 76

Factor a perfect square on the left side:
(x + -5)(x + -5) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -5) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + -5 = 8.717797887

Simplifying
x + -5 = 8.717797887

Reorder the terms:
-5 + x = 8.717797887

Solving
-5 + x = 8.717797887

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 8.717797887 + 5

Combine like terms: -5 + 5 = 0
0 + x = 8.717797887 + 5
x = 8.717797887 + 5

Combine like terms: 8.717797887 + 5 = 13.717797887
x = 13.717797887

Simplifying
x = 13.717797887


Subproblem 2
x + -5 = -8.717797887

Simplifying
x + -5 = -8.717797887

Reorder the terms:
-5 + x = -8.717797887

Solving
-5 + x = -8.717797887

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -8.717797887 + 5

Combine like terms: -5 + 5 = 0
0 + x = -8.717797887 + 5
x = -8.717797887 + 5

Combine like terms: -8.717797887 + 5 = -3.717797887
x = -3.717797887

Simplifying
x = -3.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.717797887, -3.717797887}

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