x^2+14x=28

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Solution for x^2+14x=28 equation: 


Simplifying
x2 + 14x = 28

Reorder the terms:
14x + x2 = 28

Solving
14x + x2 = 28

Solving for variable 'x'.

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

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

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 = 1.774964387
x = 1.774964387

Simplifying
x = 1.774964387


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 = -15.774964387
x = -15.774964387

Simplifying
x = -15.774964387


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

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