2x-.01x^2+.6x+30=0

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Solution for 2x-.01x^2+.6x+30=0 equation:


Simplifying
2x + -0.01x2 + 0.6x + 30 = 0

Reorder the terms:
30 + 2x + 0.6x + -0.01x2 = 0

Combine like terms: 2x + 0.6x = 2.6x
30 + 2.6x + -0.01x2 = 0

Solving
30 + 2.6x + -0.01x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.01 the coefficient of the squared term: 

Divide each side by '-0.01'.
-3000 + -260x + x2 = 0

Move the constant term to the right:

Add '3000' to each side of the equation.
-3000 + -260x + 3000 + x2 = 0 + 3000

Reorder the terms:
-3000 + 3000 + -260x + x2 = 0 + 3000

Combine like terms: -3000 + 3000 = 0
0 + -260x + x2 = 0 + 3000
-260x + x2 = 0 + 3000

Combine like terms: 0 + 3000 = 3000
-260x + x2 = 3000

The x term is -260x.  Take half its coefficient (-130).
Square it (16900) and add it to both sides.

Add '16900' to each side of the equation.
-260x + 16900 + x2 = 3000 + 16900

Reorder the terms:
16900 + -260x + x2 = 3000 + 16900

Combine like terms: 3000 + 16900 = 19900
16900 + -260x + x2 = 19900

Factor a perfect square on the left side:
(x + -130)(x + -130) = 19900

Calculate the square root of the right side: 141.067359797

Break this problem into two subproblems by setting 
(x + -130) equal to 141.067359797 and -141.067359797.

Subproblem 1

x + -130 = 141.067359797 Simplifying x + -130 = 141.067359797 Reorder the terms: -130 + x = 141.067359797 Solving -130 + x = 141.067359797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '130' to each side of the equation. -130 + 130 + x = 141.067359797 + 130 Combine like terms: -130 + 130 = 0 0 + x = 141.067359797 + 130 x = 141.067359797 + 130 Combine like terms: 141.067359797 + 130 = 271.067359797 x = 271.067359797 Simplifying x = 271.067359797

Subproblem 2

x + -130 = -141.067359797 Simplifying x + -130 = -141.067359797 Reorder the terms: -130 + x = -141.067359797 Solving -130 + x = -141.067359797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '130' to each side of the equation. -130 + 130 + x = -141.067359797 + 130 Combine like terms: -130 + 130 = 0 0 + x = -141.067359797 + 130 x = -141.067359797 + 130 Combine like terms: -141.067359797 + 130 = -11.067359797 x = -11.067359797 Simplifying x = -11.067359797

Solution

The solution to the problem is based on the solutions from the subproblems. x = {271.067359797, -11.067359797}

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