0=2x^2+8x-117

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Solution for 0=2x^2+8x-117 equation:


Simplifying
0 = 2x2 + 8x + -117

Reorder the terms:
0 = -117 + 8x + 2x2

Solving
0 = -117 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 117 = 117
117 + -8x + -2x2 = -117 + 8x + 2x2 + 117 + -8x + -2x2

Reorder the terms:
117 + -8x + -2x2 = -117 + 117 + 8x + -8x + 2x2 + -2x2

Combine like terms: -117 + 117 = 0
117 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
117 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
117 + -8x + -2x2 = 0 + 2x2 + -2x2
117 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
117 + -8x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-58.5 + 4x + x2 = 0

Move the constant term to the right:

Add '58.5' to each side of the equation.
-58.5 + 4x + 58.5 + x2 = 0 + 58.5

Reorder the terms:
-58.5 + 58.5 + 4x + x2 = 0 + 58.5

Combine like terms: -58.5 + 58.5 = 0.0
0.0 + 4x + x2 = 0 + 58.5
4x + x2 = 0 + 58.5

Combine like terms: 0 + 58.5 = 58.5
4x + x2 = 58.5

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 = 58.5 + 4

Reorder the terms:
4 + 4x + x2 = 58.5 + 4

Combine like terms: 58.5 + 4 = 62.5
4 + 4x + x2 = 62.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 62.5

Calculate the square root of the right side: 7.90569415

Break this problem into two subproblems by setting 
(x + 2) equal to 7.90569415 and -7.90569415.

Subproblem 1

x + 2 = 7.90569415 Simplifying x + 2 = 7.90569415 Reorder the terms: 2 + x = 7.90569415 Solving 2 + x = 7.90569415 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 = 7.90569415 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.90569415 + -2 x = 7.90569415 + -2 Combine like terms: 7.90569415 + -2 = 5.90569415 x = 5.90569415 Simplifying x = 5.90569415

Subproblem 2

x + 2 = -7.90569415 Simplifying x + 2 = -7.90569415 Reorder the terms: 2 + x = -7.90569415 Solving 2 + x = -7.90569415 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 = -7.90569415 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.90569415 + -2 x = -7.90569415 + -2 Combine like terms: -7.90569415 + -2 = -9.90569415 x = -9.90569415 Simplifying x = -9.90569415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.90569415, -9.90569415}

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