2x^2+15x-7.7=0

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Solution for 2x^2+15x-7.7=0 equation: 


Simplifying
2x2 + 15x + -7.7 = 0

Reorder the terms:
-7.7 + 15x + 2x2 = 0

Solving
-7.7 + 15x + 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'.
-3.85 + 7.5x + x2 = 0

Move the constant term to the right:

Add '3.85' to each side of the equation.
-3.85 + 7.5x + 3.85 + x2 = 0 + 3.85

Reorder the terms:
-3.85 + 3.85 + 7.5x + x2 = 0 + 3.85

Combine like terms: -3.85 + 3.85 = 0.00
0.00 + 7.5x + x2 = 0 + 3.85
7.5x + x2 = 0 + 3.85

Combine like terms: 0 + 3.85 = 3.85
7.5x + x2 = 3.85

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 3.85 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 3.85 + 14.0625

Combine like terms: 3.85 + 14.0625 = 17.9125
14.0625 + 7.5x + x2 = 17.9125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 17.9125

Calculate the square root of the right side: 4.232316151

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.232316151 and -4.232316151.


Subproblem 1
x + 3.75 = 4.232316151

Simplifying
x + 3.75 = 4.232316151

Reorder the terms:
3.75 + x = 4.232316151

Solving
3.75 + x = 4.232316151

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 4.232316151 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 4.232316151 + -3.75
x = 4.232316151 + -3.75

Combine like terms: 4.232316151 + -3.75 = 0.482316151
x = 0.482316151

Simplifying
x = 0.482316151


Subproblem 2
x + 3.75 = -4.232316151

Simplifying
x + 3.75 = -4.232316151

Reorder the terms:
3.75 + x = -4.232316151

Solving
3.75 + x = -4.232316151

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -4.232316151 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -4.232316151 + -3.75
x = -4.232316151 + -3.75

Combine like terms: -4.232316151 + -3.75 = -7.982316151
x = -7.982316151

Simplifying
x = -7.982316151


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.482316151, -7.982316151}

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