X^2+14X-46.5=0

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Solution for X^2+14X-46.5=0 equation: 


Simplifying
X2 + 14X + -46.5 = 0

Reorder the terms:
-46.5 + 14X + X2 = 0

Solving
-46.5 + 14X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '46.5' to each side of the equation.
-46.5 + 14X + 46.5 + X2 = 0 + 46.5

Reorder the terms:
-46.5 + 46.5 + 14X + X2 = 0 + 46.5

Combine like terms: -46.5 + 46.5 = 0.0
0.0 + 14X + X2 = 0 + 46.5
14X + X2 = 0 + 46.5

Combine like terms: 0 + 46.5 = 46.5
14X + X2 = 46.5

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 = 46.5 + 49

Reorder the terms:
49 + 14X + X2 = 46.5 + 49

Combine like terms: 46.5 + 49 = 95.5
49 + 14X + X2 = 95.5

Factor a perfect square on the left side:
(X + 7)(X + 7) = 95.5

Calculate the square root of the right side: 9.772410143

Break this problem into two subproblems by setting 
(X + 7) equal to 9.772410143 and -9.772410143.


Subproblem 1
X + 7 = 9.772410143

Simplifying
X + 7 = 9.772410143

Reorder the terms:
7 + X = 9.772410143

Solving
7 + X = 9.772410143

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 = 9.772410143 + -7

Combine like terms: 7 + -7 = 0
0 + X = 9.772410143 + -7
X = 9.772410143 + -7

Combine like terms: 9.772410143 + -7 = 2.772410143
X = 2.772410143

Simplifying
X = 2.772410143


Subproblem 2
X + 7 = -9.772410143

Simplifying
X + 7 = -9.772410143

Reorder the terms:
7 + X = -9.772410143

Solving
7 + X = -9.772410143

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 = -9.772410143 + -7

Combine like terms: 7 + -7 = 0
0 + X = -9.772410143 + -7
X = -9.772410143 + -7

Combine like terms: -9.772410143 + -7 = -16.772410143
X = -16.772410143

Simplifying
X = -16.772410143


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.772410143, -16.772410143}

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