2x^2+15x-5.7=0

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Solution for 2x^2+15x-5.7=0 equation: 


Simplifying
2x2 + 15x + -5.7 = 0

Reorder the terms:
-5.7 + 15x + 2x2 = 0

Solving
-5.7 + 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'.
-2.85 + 7.5x + x2 = 0

Move the constant term to the right:

Add '2.85' to each side of the equation.
-2.85 + 7.5x + 2.85 + x2 = 0 + 2.85

Reorder the terms:
-2.85 + 2.85 + 7.5x + x2 = 0 + 2.85

Combine like terms: -2.85 + 2.85 = 0.00
0.00 + 7.5x + x2 = 0 + 2.85
7.5x + x2 = 0 + 2.85

Combine like terms: 0 + 2.85 = 2.85
7.5x + x2 = 2.85

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 = 2.85 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 2.85 + 14.0625

Combine like terms: 2.85 + 14.0625 = 16.9125
14.0625 + 7.5x + x2 = 16.9125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 16.9125

Calculate the square root of the right side: 4.112481003

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.112481003 and -4.112481003.


Subproblem 1
x + 3.75 = 4.112481003

Simplifying
x + 3.75 = 4.112481003

Reorder the terms:
3.75 + x = 4.112481003

Solving
3.75 + x = 4.112481003

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 = 4.112481003 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 4.112481003 + -3.75
x = 4.112481003 + -3.75

Combine like terms: 4.112481003 + -3.75 = 0.362481003
x = 0.362481003

Simplifying
x = 0.362481003


Subproblem 2
x + 3.75 = -4.112481003

Simplifying
x + 3.75 = -4.112481003

Reorder the terms:
3.75 + x = -4.112481003

Solving
3.75 + x = -4.112481003

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 = -4.112481003 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -4.112481003 + -3.75
x = -4.112481003 + -3.75

Combine like terms: -4.112481003 + -3.75 = -7.862481003
x = -7.862481003

Simplifying
x = -7.862481003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.362481003, -7.862481003}

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