-X^2-12X+4=0

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Solution for -X^2-12X+4=0 equation:


Simplifying
-1X2 + -12X + 4 = 0

Reorder the terms:
4 + -12X + -1X2 = 0

Solving
4 + -12X + -1X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 12X + X2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 12X + 4 + X2 = 0 + 4

Reorder the terms:
-4 + 4 + 12X + X2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 12X + X2 = 0 + 4
12X + X2 = 0 + 4

Combine like terms: 0 + 4 = 4
12X + X2 = 4

The X term is 12X.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12X + 36 + X2 = 4 + 36

Reorder the terms:
36 + 12X + X2 = 4 + 36

Combine like terms: 4 + 36 = 40
36 + 12X + X2 = 40

Factor a perfect square on the left side:
(X + 6)(X + 6) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(X + 6) equal to 6.32455532 and -6.32455532.

Subproblem 1

X + 6 = 6.32455532 Simplifying X + 6 = 6.32455532 Reorder the terms: 6 + X = 6.32455532 Solving 6 + X = 6.32455532 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + X = 6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + X = 6.32455532 + -6 X = 6.32455532 + -6 Combine like terms: 6.32455532 + -6 = 0.32455532 X = 0.32455532 Simplifying X = 0.32455532

Subproblem 2

X + 6 = -6.32455532 Simplifying X + 6 = -6.32455532 Reorder the terms: 6 + X = -6.32455532 Solving 6 + X = -6.32455532 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + X = -6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + X = -6.32455532 + -6 X = -6.32455532 + -6 Combine like terms: -6.32455532 + -6 = -12.32455532 X = -12.32455532 Simplifying X = -12.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.32455532, -12.32455532}

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