-2x^2-2x+26.01=0

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Solution for -2x^2-2x+26.01=0 equation:


Simplifying
-2x2 + -2x + 26.01 = 0

Reorder the terms:
26.01 + -2x + -2x2 = 0

Solving
26.01 + -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'.
-13.005 + x + x2 = 0

Move the constant term to the right:

Add '13.005' to each side of the equation.
-13.005 + x + 13.005 + x2 = 0 + 13.005

Reorder the terms:
-13.005 + 13.005 + x + x2 = 0 + 13.005

Combine like terms: -13.005 + 13.005 = 0.000
0.000 + x + x2 = 0 + 13.005
x + x2 = 0 + 13.005

Combine like terms: 0 + 13.005 = 13.005
x + x2 = 13.005

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 = 13.005 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 13.005 + 0.25

Combine like terms: 13.005 + 0.25 = 13.255
1.25 + x2 = 13.255

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.255

Calculate the square root of the right side: 3.640741683

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.640741683 and -3.640741683.

Subproblem 1

x + 0.5 = 3.640741683 Simplifying x + 0.5 = 3.640741683 Reorder the terms: 0.5 + x = 3.640741683 Solving 0.5 + x = 3.640741683 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 = 3.640741683 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.640741683 + -0.5 x = 3.640741683 + -0.5 Combine like terms: 3.640741683 + -0.5 = 3.140741683 x = 3.140741683 Simplifying x = 3.140741683

Subproblem 2

x + 0.5 = -3.640741683 Simplifying x + 0.5 = -3.640741683 Reorder the terms: 0.5 + x = -3.640741683 Solving 0.5 + x = -3.640741683 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 = -3.640741683 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.640741683 + -0.5 x = -3.640741683 + -0.5 Combine like terms: -3.640741683 + -0.5 = -4.140741683 x = -4.140741683 Simplifying x = -4.140741683

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.140741683, -4.140741683}

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