2x^2+23x-8=0

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Solution for 2x^2+23x-8=0 equation:


Simplifying
2x2 + 23x + -8 = 0

Reorder the terms:
-8 + 23x + 2x2 = 0

Solving
-8 + 23x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-4 + 11.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 11.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 11.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 11.5x + x2 = 0 + 4
11.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
11.5x + x2 = 4

The x term is 11.5x.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5x + 33.0625 + x2 = 4 + 33.0625

Reorder the terms:
33.0625 + 11.5x + x2 = 4 + 33.0625

Combine like terms: 4 + 33.0625 = 37.0625
33.0625 + 11.5x + x2 = 37.0625

Factor a perfect square on the left side:
(x + 5.75)(x + 5.75) = 37.0625

Calculate the square root of the right side: 6.087897831

Break this problem into two subproblems by setting 
(x + 5.75) equal to 6.087897831 and -6.087897831.

Subproblem 1

x + 5.75 = 6.087897831 Simplifying x + 5.75 = 6.087897831 Reorder the terms: 5.75 + x = 6.087897831 Solving 5.75 + x = 6.087897831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 6.087897831 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 6.087897831 + -5.75 x = 6.087897831 + -5.75 Combine like terms: 6.087897831 + -5.75 = 0.337897831 x = 0.337897831 Simplifying x = 0.337897831

Subproblem 2

x + 5.75 = -6.087897831 Simplifying x + 5.75 = -6.087897831 Reorder the terms: 5.75 + x = -6.087897831 Solving 5.75 + x = -6.087897831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -6.087897831 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -6.087897831 + -5.75 x = -6.087897831 + -5.75 Combine like terms: -6.087897831 + -5.75 = -11.837897831 x = -11.837897831 Simplifying x = -11.837897831

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.337897831, -11.837897831}

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