-0.0055x^2+1.15x+15=0

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Solution for -0.0055x^2+1.15x+15=0 equation:


Simplifying
-0.0055x2 + 1.15x + 15 = 0

Reorder the terms:
15 + 1.15x + -0.0055x2 = 0

Solving
15 + 1.15x + -0.0055x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.0055 the coefficient of the squared term: 

Divide each side by '-0.0055'.
-2727.272727 + -209.0909091x + x2 = 0

Move the constant term to the right:

Add '2727.272727' to each side of the equation.
-2727.272727 + -209.0909091x + 2727.272727 + x2 = 0 + 2727.272727

Reorder the terms:
-2727.272727 + 2727.272727 + -209.0909091x + x2 = 0 + 2727.272727

Combine like terms: -2727.272727 + 2727.272727 = 0.000000
0.000000 + -209.0909091x + x2 = 0 + 2727.272727
-209.0909091x + x2 = 0 + 2727.272727

Combine like terms: 0 + 2727.272727 = 2727.272727
-209.0909091x + x2 = 2727.272727

The x term is -209.0909091x.  Take half its coefficient (-104.5454546).
Square it (10929.75208) and add it to both sides.

Add '10929.75208' to each side of the equation.
-209.0909091x + 10929.75208 + x2 = 2727.272727 + 10929.75208

Reorder the terms:
10929.75208 + -209.0909091x + x2 = 2727.272727 + 10929.75208

Combine like terms: 2727.272727 + 10929.75208 = 13657.024807
10929.75208 + -209.0909091x + x2 = 13657.024807

Factor a perfect square on the left side:
(x + -104.5454546)(x + -104.5454546) = 13657.024807

Calculate the square root of the right side: 116.863273987

Break this problem into two subproblems by setting 
(x + -104.5454546) equal to 116.863273987 and -116.863273987.

Subproblem 1

x + -104.5454546 = 116.863273987 Simplifying x + -104.5454546 = 116.863273987 Reorder the terms: -104.5454546 + x = 116.863273987 Solving -104.5454546 + x = 116.863273987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104.5454546' to each side of the equation. -104.5454546 + 104.5454546 + x = 116.863273987 + 104.5454546 Combine like terms: -104.5454546 + 104.5454546 = 0.0000000 0.0000000 + x = 116.863273987 + 104.5454546 x = 116.863273987 + 104.5454546 Combine like terms: 116.863273987 + 104.5454546 = 221.408728587 x = 221.408728587 Simplifying x = 221.408728587

Subproblem 2

x + -104.5454546 = -116.863273987 Simplifying x + -104.5454546 = -116.863273987 Reorder the terms: -104.5454546 + x = -116.863273987 Solving -104.5454546 + x = -116.863273987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '104.5454546' to each side of the equation. -104.5454546 + 104.5454546 + x = -116.863273987 + 104.5454546 Combine like terms: -104.5454546 + 104.5454546 = 0.0000000 0.0000000 + x = -116.863273987 + 104.5454546 x = -116.863273987 + 104.5454546 Combine like terms: -116.863273987 + 104.5454546 = -12.317819387 x = -12.317819387 Simplifying x = -12.317819387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {221.408728587, -12.317819387}

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