.05x^2+11x-125=0

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Solution for .05x^2+11x-125=0 equation:


Simplifying
0.05x2 + 11x + -125 = 0

Reorder the terms:
-125 + 11x + 0.05x2 = 0

Solving
-125 + 11x + 0.05x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.05'.
-2500 + 220x + x2 = 0

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + 220x + 2500 + x2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + 220x + x2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + 220x + x2 = 0 + 2500
220x + x2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
220x + x2 = 2500

The x term is 220x.  Take half its coefficient (110).
Square it (12100) and add it to both sides.

Add '12100' to each side of the equation.
220x + 12100 + x2 = 2500 + 12100

Reorder the terms:
12100 + 220x + x2 = 2500 + 12100

Combine like terms: 2500 + 12100 = 14600
12100 + 220x + x2 = 14600

Factor a perfect square on the left side:
(x + 110)(x + 110) = 14600

Calculate the square root of the right side: 120.830459736

Break this problem into two subproblems by setting 
(x + 110) equal to 120.830459736 and -120.830459736.

Subproblem 1

x + 110 = 120.830459736 Simplifying x + 110 = 120.830459736 Reorder the terms: 110 + x = 120.830459736 Solving 110 + x = 120.830459736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + x = 120.830459736 + -110 Combine like terms: 110 + -110 = 0 0 + x = 120.830459736 + -110 x = 120.830459736 + -110 Combine like terms: 120.830459736 + -110 = 10.830459736 x = 10.830459736 Simplifying x = 10.830459736

Subproblem 2

x + 110 = -120.830459736 Simplifying x + 110 = -120.830459736 Reorder the terms: 110 + x = -120.830459736 Solving 110 + x = -120.830459736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-110' to each side of the equation. 110 + -110 + x = -120.830459736 + -110 Combine like terms: 110 + -110 = 0 0 + x = -120.830459736 + -110 x = -120.830459736 + -110 Combine like terms: -120.830459736 + -110 = -230.830459736 x = -230.830459736 Simplifying x = -230.830459736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.830459736, -230.830459736}

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