-2x^2-2x+25.99=0

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Solution for -2x^2-2x+25.99=0 equation:


Simplifying
-2x2 + -2x + 25.99 = 0

Reorder the terms:
25.99 + -2x + -2x2 = 0

Solving
25.99 + -2x + -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'.
-12.995 + x + x2 = 0

Move the constant term to the right:

Add '12.995' to each side of the equation.
-12.995 + x + 12.995 + x2 = 0 + 12.995

Reorder the terms:
-12.995 + 12.995 + x + x2 = 0 + 12.995

Combine like terms: -12.995 + 12.995 = 0.000
0.000 + x + x2 = 0 + 12.995
x + x2 = 0 + 12.995

Combine like terms: 0 + 12.995 = 12.995
x + x2 = 12.995

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 12.995 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 12.995 + 0.25

Combine like terms: 12.995 + 0.25 = 13.245
1.25 + x2 = 13.245

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.245

Calculate the square root of the right side: 3.639368077

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.639368077 and -3.639368077.

Subproblem 1

x + 0.5 = 3.639368077 Simplifying x + 0.5 = 3.639368077 Reorder the terms: 0.5 + x = 3.639368077 Solving 0.5 + x = 3.639368077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.639368077 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.639368077 + -0.5 x = 3.639368077 + -0.5 Combine like terms: 3.639368077 + -0.5 = 3.139368077 x = 3.139368077 Simplifying x = 3.139368077

Subproblem 2

x + 0.5 = -3.639368077 Simplifying x + 0.5 = -3.639368077 Reorder the terms: 0.5 + x = -3.639368077 Solving 0.5 + x = -3.639368077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.639368077 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.639368077 + -0.5 x = -3.639368077 + -0.5 Combine like terms: -3.639368077 + -0.5 = -4.139368077 x = -4.139368077 Simplifying x = -4.139368077

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.139368077, -4.139368077}

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