2x^2+15x-9.5=0

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Solution for 2x^2+15x-9.5=0 equation: 


Simplifying
2x2 + 15x + -9.5 = 0

Reorder the terms:
-9.5 + 15x + 2x2 = 0

Solving
-9.5 + 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'.
-4.75 + 7.5x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 7.5x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 7.5x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 7.5x + x2 = 0 + 4.75
7.5x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
7.5x + x2 = 4.75

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 = 4.75 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 4.75 + 14.0625

Combine like terms: 4.75 + 14.0625 = 18.8125
14.0625 + 7.5x + x2 = 18.8125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 18.8125

Calculate the square root of the right side: 4.337337893

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.337337893 and -4.337337893.


Subproblem 1
x + 3.75 = 4.337337893

Simplifying
x + 3.75 = 4.337337893

Reorder the terms:
3.75 + x = 4.337337893

Solving
3.75 + x = 4.337337893

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 = 4.337337893 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 4.337337893 + -3.75
x = 4.337337893 + -3.75

Combine like terms: 4.337337893 + -3.75 = 0.587337893
x = 0.587337893

Simplifying
x = 0.587337893


Subproblem 2
x + 3.75 = -4.337337893

Simplifying
x + 3.75 = -4.337337893

Reorder the terms:
3.75 + x = -4.337337893

Solving
3.75 + x = -4.337337893

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 = -4.337337893 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -4.337337893 + -3.75
x = -4.337337893 + -3.75

Combine like terms: -4.337337893 + -3.75 = -8.087337893
x = -8.087337893

Simplifying
x = -8.087337893


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.587337893, -8.087337893}

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