80x^2+12x-61=0

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Solution for 80x^2+12x-61=0 equation:


Simplifying
80x2 + 12x + -61 = 0

Reorder the terms:
-61 + 12x + 80x2 = 0

Solving
-61 + 12x + 80x2 = 0

Solving for variable 'x'.

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

Divide each side by '80'.
-0.7625 + 0.15x + x2 = 0

Move the constant term to the right:

Add '0.7625' to each side of the equation.
-0.7625 + 0.15x + 0.7625 + x2 = 0 + 0.7625

Reorder the terms:
-0.7625 + 0.7625 + 0.15x + x2 = 0 + 0.7625

Combine like terms: -0.7625 + 0.7625 = 0.0000
0.0000 + 0.15x + x2 = 0 + 0.7625
0.15x + x2 = 0 + 0.7625

Combine like terms: 0 + 0.7625 = 0.7625
0.15x + x2 = 0.7625

The x term is 0.15x.  Take half its coefficient (0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
0.15x + 0.005625 + x2 = 0.7625 + 0.005625

Reorder the terms:
0.005625 + 0.15x + x2 = 0.7625 + 0.005625

Combine like terms: 0.7625 + 0.005625 = 0.768125
0.005625 + 0.15x + x2 = 0.768125

Factor a perfect square on the left side:
(x + 0.075)(x + 0.075) = 0.768125

Calculate the square root of the right side: 0.876427407

Break this problem into two subproblems by setting 
(x + 0.075) equal to 0.876427407 and -0.876427407.

Subproblem 1

x + 0.075 = 0.876427407 Simplifying x + 0.075 = 0.876427407 Reorder the terms: 0.075 + x = 0.876427407 Solving 0.075 + x = 0.876427407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.876427407 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.876427407 + -0.075 x = 0.876427407 + -0.075 Combine like terms: 0.876427407 + -0.075 = 0.801427407 x = 0.801427407 Simplifying x = 0.801427407

Subproblem 2

x + 0.075 = -0.876427407 Simplifying x + 0.075 = -0.876427407 Reorder the terms: 0.075 + x = -0.876427407 Solving 0.075 + x = -0.876427407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.876427407 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.876427407 + -0.075 x = -0.876427407 + -0.075 Combine like terms: -0.876427407 + -0.075 = -0.951427407 x = -0.951427407 Simplifying x = -0.951427407

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.801427407, -0.951427407}

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