2x^2+19x-7.5=0

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Solution for 2x^2+19x-7.5=0 equation: 


Simplifying
2x2 + 19x + -7.5 = 0

Reorder the terms:
-7.5 + 19x + 2x2 = 0

Solving
-7.5 + 19x + 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'.
-3.75 + 9.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 9.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 9.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 9.5x + x2 = 0 + 3.75
9.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
9.5x + x2 = 3.75

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = 3.75 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = 3.75 + 22.5625

Combine like terms: 3.75 + 22.5625 = 26.3125
22.5625 + 9.5x + x2 = 26.3125

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 26.3125

Calculate the square root of the right side: 5.129571132

Break this problem into two subproblems by setting 
(x + 4.75) equal to 5.129571132 and -5.129571132.


Subproblem 1
x + 4.75 = 5.129571132

Simplifying
x + 4.75 = 5.129571132

Reorder the terms:
4.75 + x = 5.129571132

Solving
4.75 + x = 5.129571132

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 5.129571132 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 5.129571132 + -4.75
x = 5.129571132 + -4.75

Combine like terms: 5.129571132 + -4.75 = 0.379571132
x = 0.379571132

Simplifying
x = 0.379571132


Subproblem 2
x + 4.75 = -5.129571132

Simplifying
x + 4.75 = -5.129571132

Reorder the terms:
4.75 + x = -5.129571132

Solving
4.75 + x = -5.129571132

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -5.129571132 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -5.129571132 + -4.75
x = -5.129571132 + -4.75

Combine like terms: -5.129571132 + -4.75 = -9.879571132
x = -9.879571132

Simplifying
x = -9.879571132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.379571132, -9.879571132}

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