0.01x^2+0.2x-0.6=0

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Solution for 0.01x^2+0.2x-0.6=0 equation:


Simplifying
0.01x2 + 0.2x + -0.6 = 0

Reorder the terms:
-0.6 + 0.2x + 0.01x2 = 0

Solving
-0.6 + 0.2x + 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'.
-60 + 20x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 20x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 20x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 20x + x2 = 0 + 60
20x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
20x + x2 = 60

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 60 + 100

Reorder the terms:
100 + 20x + x2 = 60 + 100

Combine like terms: 60 + 100 = 160
100 + 20x + x2 = 160

Factor a perfect square on the left side:
(x + 10)(x + 10) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(x + 10) equal to 12.649110641 and -12.649110641.

Subproblem 1

x + 10 = 12.649110641 Simplifying x + 10 = 12.649110641 Reorder the terms: 10 + x = 12.649110641 Solving 10 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.649110641 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.649110641 + -10 x = 12.649110641 + -10 Combine like terms: 12.649110641 + -10 = 2.649110641 x = 2.649110641 Simplifying x = 2.649110641

Subproblem 2

x + 10 = -12.649110641 Simplifying x + 10 = -12.649110641 Reorder the terms: 10 + x = -12.649110641 Solving 10 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.649110641 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.649110641 + -10 x = -12.649110641 + -10 Combine like terms: -12.649110641 + -10 = -22.649110641 x = -22.649110641 Simplifying x = -22.649110641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.649110641, -22.649110641}

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