X^2+6X-178=0

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Solution for X^2+6X-178=0 equation:


Simplifying
X2 + 6X + -178 = 0

Reorder the terms:
-178 + 6X + X2 = 0

Solving
-178 + 6X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '178' to each side of the equation.
-178 + 6X + 178 + X2 = 0 + 178

Reorder the terms:
-178 + 178 + 6X + X2 = 0 + 178

Combine like terms: -178 + 178 = 0
0 + 6X + X2 = 0 + 178
6X + X2 = 0 + 178

Combine like terms: 0 + 178 = 178
6X + X2 = 178

The X term is 6X.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6X + 9 + X2 = 178 + 9

Reorder the terms:
9 + 6X + X2 = 178 + 9

Combine like terms: 178 + 9 = 187
9 + 6X + X2 = 187

Factor a perfect square on the left side:
(X + 3)(X + 3) = 187

Calculate the square root of the right side: 13.674794331

Break this problem into two subproblems by setting 
(X + 3) equal to 13.674794331 and -13.674794331.

Subproblem 1

X + 3 = 13.674794331 Simplifying X + 3 = 13.674794331 Reorder the terms: 3 + X = 13.674794331 Solving 3 + X = 13.674794331 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 13.674794331 + -3 Combine like terms: 3 + -3 = 0 0 + X = 13.674794331 + -3 X = 13.674794331 + -3 Combine like terms: 13.674794331 + -3 = 10.674794331 X = 10.674794331 Simplifying X = 10.674794331

Subproblem 2

X + 3 = -13.674794331 Simplifying X + 3 = -13.674794331 Reorder the terms: 3 + X = -13.674794331 Solving 3 + X = -13.674794331 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = -13.674794331 + -3 Combine like terms: 3 + -3 = 0 0 + X = -13.674794331 + -3 X = -13.674794331 + -3 Combine like terms: -13.674794331 + -3 = -16.674794331 X = -16.674794331 Simplifying X = -16.674794331

Solution

The solution to the problem is based on the solutions from the subproblems. X = {10.674794331, -16.674794331}

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