0.3x+0.1-x^2=0

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Solution for 0.3x+0.1-x^2=0 equation:


Simplifying
0.3x + 0.1 + -1x2 = 0

Reorder the terms:
0.1 + 0.3x + -1x2 = 0

Solving
0.1 + 0.3x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.1 + -0.3x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.3x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.3x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.3x + x2 = 0 + 0.1
-0.3x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.3x + x2 = 0.1

The x term is -0.3x.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3x + 0.0225 + x2 = 0.1 + 0.0225

Reorder the terms:
0.0225 + -0.3x + x2 = 0.1 + 0.0225

Combine like terms: 0.1 + 0.0225 = 0.1225
0.0225 + -0.3x + x2 = 0.1225

Factor a perfect square on the left side:
(x + -0.15)(x + -0.15) = 0.1225

Calculate the square root of the right side: 0.35

Break this problem into two subproblems by setting 
(x + -0.15) equal to 0.35 and -0.35.

Subproblem 1

x + -0.15 = 0.35 Simplifying x + -0.15 = 0.35 Reorder the terms: -0.15 + x = 0.35 Solving -0.15 + x = 0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.35 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.35 + 0.15 x = 0.35 + 0.15 Combine like terms: 0.35 + 0.15 = 0.5 x = 0.5 Simplifying x = 0.5

Subproblem 2

x + -0.15 = -0.35 Simplifying x + -0.15 = -0.35 Reorder the terms: -0.15 + x = -0.35 Solving -0.15 + x = -0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.35 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.35 + 0.15 x = -0.35 + 0.15 Combine like terms: -0.35 + 0.15 = -0.2 x = -0.2 Simplifying x = -0.2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5, -0.2}

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