x^2+0.3x-1.80=0

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Solution for x^2+0.3x-1.80=0 equation:


Simplifying
x2 + 0.3x + -1.80 = 0

Reorder the terms:
-1.80 + 0.3x + x2 = 0

Solving
-1.80 + 0.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.80' to each side of the equation.
-1.80 + 0.3x + 1.80 + x2 = 0 + 1.80

Reorder the terms:
-1.80 + 1.80 + 0.3x + x2 = 0 + 1.80

Combine like terms: -1.80 + 1.80 = 0.00
0.00 + 0.3x + x2 = 0 + 1.80
0.3x + x2 = 0 + 1.80

Combine like terms: 0 + 1.80 = 1.8
0.3x + x2 = 1.8

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 = 1.8 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 1.8 + 0.0225

Combine like terms: 1.8 + 0.0225 = 1.8225
0.0225 + 0.3x + x2 = 1.8225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 1.8225

Calculate the square root of the right side: 1.35

Break this problem into two subproblems by setting 
(x + 0.15) equal to 1.35 and -1.35.

Subproblem 1

x + 0.15 = 1.35 Simplifying x + 0.15 = 1.35 Reorder the terms: 0.15 + x = 1.35 Solving 0.15 + x = 1.35 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 = 1.35 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.35 + -0.15 x = 1.35 + -0.15 Combine like terms: 1.35 + -0.15 = 1.2 x = 1.2 Simplifying x = 1.2

Subproblem 2

x + 0.15 = -1.35 Simplifying x + 0.15 = -1.35 Reorder the terms: 0.15 + x = -1.35 Solving 0.15 + x = -1.35 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 = -1.35 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.35 + -0.15 x = -1.35 + -0.15 Combine like terms: -1.35 + -0.15 = -1.5 x = -1.5 Simplifying x = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2, -1.5}

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