x^2-4x-51=0

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Solution for x^2-4x-51=0 equation: 


Simplifying
x2 + -4x + -51 = 0

Reorder the terms:
-51 + -4x + x2 = 0

Solving
-51 + -4x + 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 + -4x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -4x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -4x + x2 = 0 + 51
-4x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-4x + x2 = 51

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 51 + 4

Reorder the terms:
4 + -4x + x2 = 51 + 4

Combine like terms: 51 + 4 = 55
4 + -4x + x2 = 55

Factor a perfect square on the left side:
(x + -2)(x + -2) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + -2) equal to 7.416198487 and -7.416198487.


Subproblem 1
x + -2 = 7.416198487

Simplifying
x + -2 = 7.416198487

Reorder the terms:
-2 + x = 7.416198487

Solving
-2 + x = 7.416198487

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 7.416198487 + 2

Combine like terms: -2 + 2 = 0
0 + x = 7.416198487 + 2
x = 7.416198487 + 2

Combine like terms: 7.416198487 + 2 = 9.416198487
x = 9.416198487

Simplifying
x = 9.416198487


Subproblem 2
x + -2 = -7.416198487

Simplifying
x + -2 = -7.416198487

Reorder the terms:
-2 + x = -7.416198487

Solving
-2 + x = -7.416198487

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -7.416198487 + 2

Combine like terms: -2 + 2 = 0
0 + x = -7.416198487 + 2
x = -7.416198487 + 2

Combine like terms: -7.416198487 + 2 = -5.416198487
x = -5.416198487

Simplifying
x = -5.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.416198487, -5.416198487}

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