x^2+0.6x+0.09=0

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Solution for x^2+0.6x+0.09=0 equation:


Simplifying
x2 + 0.6x + 0.09 = 0

Reorder the terms:
0.09 + 0.6x + x2 = 0

Solving
0.09 + 0.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.09' to each side of the equation.
0.09 + 0.6x + -0.09 + x2 = 0 + -0.09

Reorder the terms:
0.09 + -0.09 + 0.6x + x2 = 0 + -0.09

Combine like terms: 0.09 + -0.09 = 0.00
0.00 + 0.6x + x2 = 0 + -0.09
0.6x + x2 = 0 + -0.09

Combine like terms: 0 + -0.09 = -0.09
0.6x + x2 = -0.09

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = -0.09 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = -0.09 + 0.09

Combine like terms: -0.09 + 0.09 = 0.00
0.09 + 0.6x + x2 = 0.00

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.00 and 0.00.

Subproblem 1

x + 0.3 = 0.00 Simplifying x + 0.3 = 0.00 Reorder the terms: 0.3 + x = 0.00 Solving 0.3 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.00 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.00 + -0.3 x = 0.00 + -0.3 Combine like terms: 0.00 + -0.3 = -0.3 x = -0.3 Simplifying x = -0.3

Subproblem 2

x + 0.3 = 0.00 Simplifying x + 0.3 = 0.00 Reorder the terms: 0.3 + x = 0.00 Solving 0.3 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.00 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.00 + -0.3 x = 0.00 + -0.3 Combine like terms: 0.00 + -0.3 = -0.3 x = -0.3 Simplifying x = -0.3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.3, -0.3}

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