x^2-1.3x+.3=0

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


Simplifying
x2 + -1.3x + 0.3 = 0

Reorder the terms:
0.3 + -1.3x + x2 = 0

Solving
0.3 + -1.3x + 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 + -1.3x + -0.3 + x2 = 0 + -0.3

Reorder the terms:
0.3 + -0.3 + -1.3x + x2 = 0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -1.3x + x2 = 0 + -0.3
-1.3x + x2 = 0 + -0.3

Combine like terms: 0 + -0.3 = -0.3
-1.3x + x2 = -0.3

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 = -0.3 + 0.4225

Reorder the terms:
0.4225 + -1.3x + x2 = -0.3 + 0.4225

Combine like terms: -0.3 + 0.4225 = 0.1225
0.4225 + -1.3x + x2 = 0.1225

Factor a perfect square on the left side:
(x + -0.65)(x + -0.65) = 0.1225

Calculate the square root of the right side: 0.35

Break this problem into two subproblems by setting 
(x + -0.65) equal to 0.35 and -0.35.

Subproblem 1

x + -0.65 = 0.35 Simplifying x + -0.65 = 0.35 Reorder the terms: -0.65 + x = 0.35 Solving -0.65 + x = 0.35 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 = 0.35 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 0.35 + 0.65 x = 0.35 + 0.65 Combine like terms: 0.35 + 0.65 = 1 x = 1 Simplifying x = 1

Subproblem 2

x + -0.65 = -0.35 Simplifying x + -0.65 = -0.35 Reorder the terms: -0.65 + x = -0.35 Solving -0.65 + x = -0.35 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 = -0.35 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -0.35 + 0.65 x = -0.35 + 0.65 Combine like terms: -0.35 + 0.65 = 0.3 x = 0.3 Simplifying x = 0.3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1, 0.3}

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