186=2x^2-8x+13

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Solution for 186=2x^2-8x+13 equation:


Simplifying
186 = 2x2 + -8x + 13

Reorder the terms:
186 = 13 + -8x + 2x2

Solving
186 = 13 + -8x + 2x2

Solving for variable 'x'.

Combine like terms: 186 + -13 = 173
173 + 8x + -2x2 = 13 + -8x + 2x2 + -13 + 8x + -2x2

Reorder the terms:
173 + 8x + -2x2 = 13 + -13 + -8x + 8x + 2x2 + -2x2

Combine like terms: 13 + -13 = 0
173 + 8x + -2x2 = 0 + -8x + 8x + 2x2 + -2x2
173 + 8x + -2x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
173 + 8x + -2x2 = 0 + 2x2 + -2x2
173 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
173 + 8x + -2x2 = 0

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

Divide each side by '-2'.
-86.5 + -4x + x2 = 0

Move the constant term to the right:

Add '86.5' to each side of the equation.
-86.5 + -4x + 86.5 + x2 = 0 + 86.5

Reorder the terms:
-86.5 + 86.5 + -4x + x2 = 0 + 86.5

Combine like terms: -86.5 + 86.5 = 0.0
0.0 + -4x + x2 = 0 + 86.5
-4x + x2 = 0 + 86.5

Combine like terms: 0 + 86.5 = 86.5
-4x + x2 = 86.5

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 = 86.5 + 4

Reorder the terms:
4 + -4x + x2 = 86.5 + 4

Combine like terms: 86.5 + 4 = 90.5
4 + -4x + x2 = 90.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 90.5

Calculate the square root of the right side: 9.513148795

Break this problem into two subproblems by setting 
(x + -2) equal to 9.513148795 and -9.513148795.

Subproblem 1

x + -2 = 9.513148795 Simplifying x + -2 = 9.513148795 Reorder the terms: -2 + x = 9.513148795 Solving -2 + x = 9.513148795 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 = 9.513148795 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.513148795 + 2 x = 9.513148795 + 2 Combine like terms: 9.513148795 + 2 = 11.513148795 x = 11.513148795 Simplifying x = 11.513148795

Subproblem 2

x + -2 = -9.513148795 Simplifying x + -2 = -9.513148795 Reorder the terms: -2 + x = -9.513148795 Solving -2 + x = -9.513148795 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 = -9.513148795 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.513148795 + 2 x = -9.513148795 + 2 Combine like terms: -9.513148795 + 2 = -7.513148795 x = -7.513148795 Simplifying x = -7.513148795

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.513148795, -7.513148795}

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