2x^2+12.5x-10.5=0

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Solution for 2x^2+12.5x-10.5=0 equation:


Simplifying
2x2 + 12.5x + -10.5 = 0

Reorder the terms:
-10.5 + 12.5x + 2x2 = 0

Solving
-10.5 + 12.5x + 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'.
-5.25 + 6.25x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + 6.25x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + 6.25x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + 6.25x + x2 = 0 + 5.25
6.25x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
6.25x + x2 = 5.25

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = 5.25 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = 5.25 + 9.765625

Combine like terms: 5.25 + 9.765625 = 15.015625
9.765625 + 6.25x + x2 = 15.015625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 15.015625

Calculate the square root of the right side: 3.875

Break this problem into two subproblems by setting 
(x + 3.125) equal to 3.875 and -3.875.


Subproblem 1
x + 3.125 = 3.875

Simplifying
x + 3.125 = 3.875

Reorder the terms:
3.125 + x = 3.875

Solving
3.125 + x = 3.875

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 3.875 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 3.875 + -3.125
x = 3.875 + -3.125

Combine like terms: 3.875 + -3.125 = 0.75
x = 0.75

Simplifying
x = 0.75


Subproblem 2
x + 3.125 = -3.875

Simplifying
x + 3.125 = -3.875

Reorder the terms:
3.125 + x = -3.875

Solving
3.125 + x = -3.875

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -3.875 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -3.875 + -3.125
x = -3.875 + -3.125

Combine like terms: -3.875 + -3.125 = -7
x = -7

Simplifying
x = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.75, -7}

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