x^2+.1x-.3=0

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Solution for x^2+.1x-.3=0 equation:


Simplifying
x2 + 0.1x + -0.3 = 0

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

Solving
-0.3 + 0.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 0.1x.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1x + 0.0025 + x2 = 0.3 + 0.0025

Reorder the terms:
0.0025 + 0.1x + x2 = 0.3 + 0.0025

Combine like terms: 0.3 + 0.0025 = 0.3025
0.0025 + 0.1x + x2 = 0.3025

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.3025

Calculate the square root of the right side: 0.55

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.55 and -0.55.

Subproblem 1

x + 0.05 = 0.55 Simplifying x + 0.05 = 0.55 Reorder the terms: 0.05 + x = 0.55 Solving 0.05 + x = 0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.55 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.55 + -0.05 x = 0.55 + -0.05 Combine like terms: 0.55 + -0.05 = 0.5 x = 0.5 Simplifying x = 0.5

Subproblem 2

x + 0.05 = -0.55 Simplifying x + 0.05 = -0.55 Reorder the terms: 0.05 + x = -0.55 Solving 0.05 + x = -0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.55 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.55 + -0.05 x = -0.55 + -0.05 Combine like terms: -0.55 + -0.05 = -0.6 x = -0.6 Simplifying x = -0.6

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5, -0.6}

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