0.03x^2+0.6x-6=3

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Solution for 0.03x^2+0.6x-6=3 equation:


Simplifying
0.03x2 + 0.6x + -6 = 3

Reorder the terms:
-6 + 0.6x + 0.03x2 = 3

Solving
-6 + 0.6x + 0.03x2 = 3

Solving for variable 'x'.

Reorder the terms:
-6 + -3 + 0.6x + 0.03x2 = 3 + -3

Combine like terms: -6 + -3 = -9
-9 + 0.6x + 0.03x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-9 + 0.6x + 0.03x2 = 0

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

Divide each side by '0.03'.
-300 + 20x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 20x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 20x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 20x + x2 = 0 + 300
20x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
20x + x2 = 300

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 = 300 + 100

Reorder the terms:
100 + 20x + x2 = 300 + 100

Combine like terms: 300 + 100 = 400
100 + 20x + x2 = 400

Factor a perfect square on the left side:
(x + 10)(x + 10) = 400

Calculate the square root of the right side: 20

Break this problem into two subproblems by setting 
(x + 10) equal to 20 and -20.

Subproblem 1

x + 10 = 20 Simplifying x + 10 = 20 Reorder the terms: 10 + x = 20 Solving 10 + x = 20 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 = 20 + -10 Combine like terms: 10 + -10 = 0 0 + x = 20 + -10 x = 20 + -10 Combine like terms: 20 + -10 = 10 x = 10 Simplifying x = 10

Subproblem 2

x + 10 = -20 Simplifying x + 10 = -20 Reorder the terms: 10 + x = -20 Solving 10 + x = -20 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 = -20 + -10 Combine like terms: 10 + -10 = 0 0 + x = -20 + -10 x = -20 + -10 Combine like terms: -20 + -10 = -30 x = -30 Simplifying x = -30

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10, -30}

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