0=.5x^2-3x+1

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Solution for 0=.5x^2-3x+1 equation:


Simplifying
0 = 0.5x2 + -3x + 1

Reorder the terms:
0 = 1 + -3x + 0.5x2

Solving
0 = 1 + -3x + 0.5x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 3x + -0.5x2 = 1 + -3x + 0.5x2 + -1 + 3x + -0.5x2

Reorder the terms:
-1 + 3x + -0.5x2 = 1 + -1 + -3x + 3x + 0.5x2 + -0.5x2

Combine like terms: 1 + -1 = 0
-1 + 3x + -0.5x2 = 0 + -3x + 3x + 0.5x2 + -0.5x2
-1 + 3x + -0.5x2 = -3x + 3x + 0.5x2 + -0.5x2

Combine like terms: -3x + 3x = 0
-1 + 3x + -0.5x2 = 0 + 0.5x2 + -0.5x2
-1 + 3x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
-1 + 3x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
2 + -6x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -6x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6x + x2 = 0 + -2
-6x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6x + x2 = -2

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2 + 9

Reorder the terms:
9 + -6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6x + x2 = 7

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -3 = 2.645751311 Simplifying x + -3 = 2.645751311 Reorder the terms: -3 + x = 2.645751311 Solving -3 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.645751311 + 3 x = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x = 5.645751311 Simplifying x = 5.645751311

Subproblem 2

x + -3 = -2.645751311 Simplifying x + -3 = -2.645751311 Reorder the terms: -3 + x = -2.645751311 Solving -3 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.645751311 + 3 x = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x = 0.354248689 Simplifying x = 0.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.645751311, 0.354248689}

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