-0.3x^2-0.6x+3000=0

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Solution for -0.3x^2-0.6x+3000=0 equation:


Simplifying
-0.3x2 + -0.6x + 3000 = 0

Reorder the terms:
3000 + -0.6x + -0.3x2 = 0

Solving
3000 + -0.6x + -0.3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
-10000 + 2x + x2 = 0

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + 2x + 10000 + x2 = 0 + 10000

Reorder the terms:
-10000 + 10000 + 2x + x2 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + 2x + x2 = 0 + 10000
2x + x2 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
2x + x2 = 10000

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 10000 + 1

Reorder the terms:
1 + 2x + x2 = 10000 + 1

Combine like terms: 10000 + 1 = 10001
1 + 2x + x2 = 10001

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10001

Calculate the square root of the right side: 100.004999875

Break this problem into two subproblems by setting 
(x + 1) equal to 100.004999875 and -100.004999875.

Subproblem 1

x + 1 = 100.004999875 Simplifying x + 1 = 100.004999875 Reorder the terms: 1 + x = 100.004999875 Solving 1 + x = 100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 100.004999875 + -1 Combine like terms: 1 + -1 = 0 0 + x = 100.004999875 + -1 x = 100.004999875 + -1 Combine like terms: 100.004999875 + -1 = 99.004999875 x = 99.004999875 Simplifying x = 99.004999875

Subproblem 2

x + 1 = -100.004999875 Simplifying x + 1 = -100.004999875 Reorder the terms: 1 + x = -100.004999875 Solving 1 + x = -100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -100.004999875 + -1 Combine like terms: 1 + -1 = 0 0 + x = -100.004999875 + -1 x = -100.004999875 + -1 Combine like terms: -100.004999875 + -1 = -101.004999875 x = -101.004999875 Simplifying x = -101.004999875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {99.004999875, -101.004999875}

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