.5x^2=2x-.3

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


Simplifying
0.5x2 = 2x + -0.3

Reorder the terms:
0.5x2 = -0.3 + 2x

Solving
0.5x2 = -0.3 + 2x

Solving for variable 'x'.

Reorder the terms:
0.3 + -2x + 0.5x2 = -0.3 + 2x + 0.3 + -2x

Reorder the terms:
0.3 + -2x + 0.5x2 = -0.3 + 0.3 + 2x + -2x

Combine like terms: -0.3 + 0.3 = 0.0
0.3 + -2x + 0.5x2 = 0.0 + 2x + -2x
0.3 + -2x + 0.5x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
0.3 + -2x + 0.5x2 = 0

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

Divide each side by '0.5'.
0.6 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -4x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -4x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -4x + x2 = 0 + -0.6
-4x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-4x + x2 = -0.6

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -0.6 + 4

Reorder the terms:
4 + -4x + x2 = -0.6 + 4

Combine like terms: -0.6 + 4 = 3.4
4 + -4x + x2 = 3.4

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.4

Calculate the square root of the right side: 1.843908891

Break this problem into two subproblems by setting 
(x + -2) equal to 1.843908891 and -1.843908891.

Subproblem 1

x + -2 = 1.843908891 Simplifying x + -2 = 1.843908891 Reorder the terms: -2 + x = 1.843908891 Solving -2 + x = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.843908891 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.843908891 + 2 x = 1.843908891 + 2 Combine like terms: 1.843908891 + 2 = 3.843908891 x = 3.843908891 Simplifying x = 3.843908891

Subproblem 2

x + -2 = -1.843908891 Simplifying x + -2 = -1.843908891 Reorder the terms: -2 + x = -1.843908891 Solving -2 + x = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.843908891 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.843908891 + 2 x = -1.843908891 + 2 Combine like terms: -1.843908891 + 2 = 0.156091109 x = 0.156091109 Simplifying x = 0.156091109

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.843908891, 0.156091109}

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