2x^2+2x-1=61

Solution for 2x^2+2x-1=61 equation:

Simplifying
2x2 + 2x + -1 = 61

Reorder the terms:
-1 + 2x + 2x2 = 61

Solving
-1 + 2x + 2x2 = 61

Solving for variable 'x'.

Reorder the terms:
-1 + -61 + 2x + 2x2 = 61 + -61

Combine like terms: -1 + -61 = -62
-62 + 2x + 2x2 = 61 + -61

Combine like terms: 61 + -61 = 0
-62 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + x + x2)' equal to zero and attempt to solve:

Simplifying
-31 + x + x2 = 0

Solving
-31 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + x + x2 = 0 + 31
x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
x + x2 = 31

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.
x + 0.25 + x2 = 31 + 0.25

Reorder the terms:
0.25 + x + x2 = 31 + 0.25

Combine like terms: 31 + 0.25 = 31.25
0.25 + x + x2 = 31.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.590169944 and -5.590169944.

Subproblem 1
x + 0.5 = 5.590169944

Simplifying
x + 0.5 = 5.590169944

Reorder the terms:
0.5 + x = 5.590169944

Solving
0.5 + x = 5.590169944

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 = 5.590169944 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.590169944 + -0.5
x = 5.590169944 + -0.5

Combine like terms: 5.590169944 + -0.5 = 5.090169944
x = 5.090169944

Simplifying
x = 5.090169944

Subproblem 2
x + 0.5 = -5.590169944

Simplifying
x + 0.5 = -5.590169944

Reorder the terms:
0.5 + x = -5.590169944

Solving
0.5 + x = -5.590169944

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 = -5.590169944 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.590169944 + -0.5
x = -5.590169944 + -0.5

Combine like terms: -5.590169944 + -0.5 = -6.090169944
x = -6.090169944

Simplifying
x = -6.090169944

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.090169944, -6.090169944}
Solution
x = {5.090169944, -6.090169944}