2x^2+25x-7.5=0

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Solution for 2x^2+25x-7.5=0 equation: 


Simplifying
2x2 + 25x + -7.5 = 0

Reorder the terms:
-7.5 + 25x + 2x2 = 0

Solving
-7.5 + 25x + 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 + 12.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 12.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 12.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 12.5x + x2 = 0 + 3.75
12.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
12.5x + x2 = 3.75

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = 3.75 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 3.75 + 39.0625

Combine like terms: 3.75 + 39.0625 = 42.8125
39.0625 + 12.5x + x2 = 42.8125

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 42.8125

Calculate the square root of the right side: 6.543126164

Break this problem into two subproblems by setting 
(x + 6.25) equal to 6.543126164 and -6.543126164.


Subproblem 1
x + 6.25 = 6.543126164

Simplifying
x + 6.25 = 6.543126164

Reorder the terms:
6.25 + x = 6.543126164

Solving
6.25 + x = 6.543126164

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 6.543126164 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 6.543126164 + -6.25
x = 6.543126164 + -6.25

Combine like terms: 6.543126164 + -6.25 = 0.293126164
x = 0.293126164

Simplifying
x = 0.293126164


Subproblem 2
x + 6.25 = -6.543126164

Simplifying
x + 6.25 = -6.543126164

Reorder the terms:
6.25 + x = -6.543126164

Solving
6.25 + x = -6.543126164

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -6.543126164 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -6.543126164 + -6.25
x = -6.543126164 + -6.25

Combine like terms: -6.543126164 + -6.25 = -12.793126164
x = -12.793126164

Simplifying
x = -12.793126164


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.293126164, -12.793126164}

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