x^2+14x-54=0

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Solution for x^2+14x-54=0 equation:


Simplifying
x2 + 14x + -54 = 0

Reorder the terms:
-54 + 14x + x2 = 0

Solving
-54 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 14x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 14x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 14x + x2 = 0 + 54
14x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
14x + x2 = 54

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 = 54 + 49

Reorder the terms:
49 + 14x + x2 = 54 + 49

Combine like terms: 54 + 49 = 103
49 + 14x + x2 = 103

Factor a perfect square on the left side:
(x + 7)(x + 7) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(x + 7) equal to 10.148891565 and -10.148891565.


Subproblem 1
x + 7 = 10.148891565

Simplifying
x + 7 = 10.148891565

Reorder the terms:
7 + x = 10.148891565

Solving
7 + x = 10.148891565

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 = 10.148891565 + -7

Combine like terms: 7 + -7 = 0
0 + x = 10.148891565 + -7
x = 10.148891565 + -7

Combine like terms: 10.148891565 + -7 = 3.148891565
x = 3.148891565

Simplifying
x = 3.148891565


Subproblem 2
x + 7 = -10.148891565

Simplifying
x + 7 = -10.148891565

Reorder the terms:
7 + x = -10.148891565

Solving
7 + x = -10.148891565

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 = -10.148891565 + -7

Combine like terms: 7 + -7 = 0
0 + x = -10.148891565 + -7
x = -10.148891565 + -7

Combine like terms: -10.148891565 + -7 = -17.148891565
x = -17.148891565

Simplifying
x = -17.148891565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.148891565, -17.148891565}

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