2x^2-4x-61=0

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Solution for 2x^2-4x-61=0 equation:


Simplifying
2x2 + -4x + -61 = 0

Reorder the terms:
-61 + -4x + 2x2 = 0

Solving
-61 + -4x + 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'.
-30.5 + -2x + x2 = 0

Move the constant term to the right:

Add '30.5' to each side of the equation.
-30.5 + -2x + 30.5 + x2 = 0 + 30.5

Reorder the terms:
-30.5 + 30.5 + -2x + x2 = 0 + 30.5

Combine like terms: -30.5 + 30.5 = 0.0
0.0 + -2x + x2 = 0 + 30.5
-2x + x2 = 0 + 30.5

Combine like terms: 0 + 30.5 = 30.5
-2x + x2 = 30.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 30.5 + 1

Reorder the terms:
1 + -2x + x2 = 30.5 + 1

Combine like terms: 30.5 + 1 = 31.5
1 + -2x + x2 = 31.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 31.5

Calculate the square root of the right side: 5.61248608

Break this problem into two subproblems by setting 
(x + -1) equal to 5.61248608 and -5.61248608.

Subproblem 1

x + -1 = 5.61248608 Simplifying x + -1 = 5.61248608 Reorder the terms: -1 + x = 5.61248608 Solving -1 + x = 5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.61248608 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.61248608 + 1 x = 5.61248608 + 1 Combine like terms: 5.61248608 + 1 = 6.61248608 x = 6.61248608 Simplifying x = 6.61248608

Subproblem 2

x + -1 = -5.61248608 Simplifying x + -1 = -5.61248608 Reorder the terms: -1 + x = -5.61248608 Solving -1 + x = -5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.61248608 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.61248608 + 1 x = -5.61248608 + 1 Combine like terms: -5.61248608 + 1 = -4.61248608 x = -4.61248608 Simplifying x = -4.61248608

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.61248608, -4.61248608}

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