x^2-14x-28=0

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Solution for x^2-14x-28=0 equation: 


Simplifying
x2 + -14x + -28 = 0

Reorder the terms:
-28 + -14x + x2 = 0

Solving
-28 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -14x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -14x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -14x + x2 = 0 + 28
-14x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-14x + x2 = 28

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 28 + 49

Reorder the terms:
49 + -14x + x2 = 28 + 49

Combine like terms: 28 + 49 = 77
49 + -14x + x2 = 77

Factor a perfect square on the left side:
(x + -7)(x + -7) = 77

Calculate the square root of the right side: 8.774964387

Break this problem into two subproblems by setting 
(x + -7) equal to 8.774964387 and -8.774964387.


Subproblem 1
x + -7 = 8.774964387

Simplifying
x + -7 = 8.774964387

Reorder the terms:
-7 + x = 8.774964387

Solving
-7 + x = 8.774964387

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 8.774964387 + 7

Combine like terms: -7 + 7 = 0
0 + x = 8.774964387 + 7
x = 8.774964387 + 7

Combine like terms: 8.774964387 + 7 = 15.774964387
x = 15.774964387

Simplifying
x = 15.774964387


Subproblem 2
x + -7 = -8.774964387

Simplifying
x + -7 = -8.774964387

Reorder the terms:
-7 + x = -8.774964387

Solving
-7 + x = -8.774964387

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -8.774964387 + 7

Combine like terms: -7 + 7 = 0
0 + x = -8.774964387 + 7
x = -8.774964387 + 7

Combine like terms: -8.774964387 + 7 = -1.774964387
x = -1.774964387

Simplifying
x = -1.774964387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.774964387, -1.774964387}

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