x^2+1.3x-3=0

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Solution for x^2+1.3x-3=0 equation: 


Simplifying
x2 + 1.3x + -3 = 0

Reorder the terms:
-3 + 1.3x + x2 = 0

Solving
-3 + 1.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.3x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.3x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.3x + x2 = 0 + 3
1.3x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.3x + x2 = 3

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 3 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 3 + 0.4225

Combine like terms: 3 + 0.4225 = 3.4225
0.4225 + 1.3x + x2 = 3.4225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 3.4225

Calculate the square root of the right side: 1.85

Break this problem into two subproblems by setting 
(x + 0.65) equal to 1.85 and -1.85.


Subproblem 1
x + 0.65 = 1.85

Simplifying
x + 0.65 = 1.85

Reorder the terms:
0.65 + x = 1.85

Solving
0.65 + x = 1.85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 1.85 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 1.85 + -0.65
x = 1.85 + -0.65

Combine like terms: 1.85 + -0.65 = 1.2
x = 1.2

Simplifying
x = 1.2


Subproblem 2
x + 0.65 = -1.85

Simplifying
x + 0.65 = -1.85

Reorder the terms:
0.65 + x = -1.85

Solving
0.65 + x = -1.85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -1.85 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -1.85 + -0.65
x = -1.85 + -0.65

Combine like terms: -1.85 + -0.65 = -2.5
x = -2.5

Simplifying
x = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, -2.5}

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