125+12.5x-0.30x^2=

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Solution for 125+12.5x-0.30x^2= equation: 


Simplifying
125 + 12.5x + -0.30x2 = 0

Solving
125 + 12.5x + -0.30x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.30 the coefficient of the squared term: 

Divide each side by '-0.30'.
-416.6666667 + -41.66666667x + x2 = 0

Move the constant term to the right:

Add '416.6666667' to each side of the equation.
-416.6666667 + -41.66666667x + 416.6666667 + x2 = 0 + 416.6666667

Reorder the terms:
-416.6666667 + 416.6666667 + -41.66666667x + x2 = 0 + 416.6666667

Combine like terms: -416.6666667 + 416.6666667 = 0.0000000
0.0000000 + -41.66666667x + x2 = 0 + 416.6666667
-41.66666667x + x2 = 0 + 416.6666667

Combine like terms: 0 + 416.6666667 = 416.6666667
-41.66666667x + x2 = 416.6666667

The x term is -41.66666667x.  Take half its coefficient (-20.83333334).
Square it (434.0277781) and add it to both sides.

Add '434.0277781' to each side of the equation.
-41.66666667x + 434.0277781 + x2 = 416.6666667 + 434.0277781

Reorder the terms:
434.0277781 + -41.66666667x + x2 = 416.6666667 + 434.0277781

Combine like terms: 416.6666667 + 434.0277781 = 850.6944448
434.0277781 + -41.66666667x + x2 = 850.6944448

Factor a perfect square on the left side:
(x + -20.83333334)(x + -20.83333334) = 850.6944448

Calculate the square root of the right side: 29.166666673

Break this problem into two subproblems by setting 
(x + -20.83333334) equal to 29.166666673 and -29.166666673.


Subproblem 1
x + -20.83333334 = 29.166666673

Simplifying
x + -20.83333334 = 29.166666673

Reorder the terms:
-20.83333334 + x = 29.166666673

Solving
-20.83333334 + x = 29.166666673

Solving for variable 'x'.

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

Add '20.83333334' to each side of the equation.
-20.83333334 + 20.83333334 + x = 29.166666673 + 20.83333334

Combine like terms: -20.83333334 + 20.83333334 = 0.00000000
0.00000000 + x = 29.166666673 + 20.83333334
x = 29.166666673 + 20.83333334

Combine like terms: 29.166666673 + 20.83333334 = 50.000000013
x = 50.000000013

Simplifying
x = 50.000000013


Subproblem 2
x + -20.83333334 = -29.166666673

Simplifying
x + -20.83333334 = -29.166666673

Reorder the terms:
-20.83333334 + x = -29.166666673

Solving
-20.83333334 + x = -29.166666673

Solving for variable 'x'.

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

Add '20.83333334' to each side of the equation.
-20.83333334 + 20.83333334 + x = -29.166666673 + 20.83333334

Combine like terms: -20.83333334 + 20.83333334 = 0.00000000
0.00000000 + x = -29.166666673 + 20.83333334
x = -29.166666673 + 20.83333334

Combine like terms: -29.166666673 + 20.83333334 = -8.333333333
x = -8.333333333

Simplifying
x = -8.333333333


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.000000013, -8.333333333}

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