X^2-102=-4X

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Solution for X^2-102=-4X equation: 


Simplifying
X2 + -102 = -4X

Reorder the terms:
-102 + X2 = -4X

Solving
-102 + X2 = -4X

Solving for variable 'X'.

Reorder the terms:
-102 + 4X + X2 = -4X + 4X

Combine like terms: -4X + 4X = 0
-102 + 4X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 4X + 102 + X2 = 0 + 102

Reorder the terms:
-102 + 102 + 4X + X2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 4X + X2 = 0 + 102
4X + X2 = 0 + 102

Combine like terms: 0 + 102 = 102
4X + X2 = 102

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 = 102 + 4

Reorder the terms:
4 + 4X + X2 = 102 + 4

Combine like terms: 102 + 4 = 106
4 + 4X + X2 = 106

Factor a perfect square on the left side:
(X + 2)(X + 2) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(X + 2) equal to 10.295630141 and -10.295630141.


Subproblem 1
X + 2 = 10.295630141

Simplifying
X + 2 = 10.295630141

Reorder the terms:
2 + X = 10.295630141

Solving
2 + X = 10.295630141

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 = 10.295630141 + -2

Combine like terms: 2 + -2 = 0
0 + X = 10.295630141 + -2
X = 10.295630141 + -2

Combine like terms: 10.295630141 + -2 = 8.295630141
X = 8.295630141

Simplifying
X = 8.295630141


Subproblem 2
X + 2 = -10.295630141

Simplifying
X + 2 = -10.295630141

Reorder the terms:
2 + X = -10.295630141

Solving
2 + X = -10.295630141

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 = -10.295630141 + -2

Combine like terms: 2 + -2 = 0
0 + X = -10.295630141 + -2
X = -10.295630141 + -2

Combine like terms: -10.295630141 + -2 = -12.295630141
X = -12.295630141

Simplifying
X = -12.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {8.295630141, -12.295630141}

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