0=2*x^2-4*x+1.5

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Solution for 0=2*x^2-4*x+1.5 equation:


Simplifying
0 = 2x2 + -4x + 1.5

Reorder the terms:
0 = 1.5 + -4x + 2x2

Solving
0 = 1.5 + -4x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -1.5 = -1.5
-1.5 + 4x + -2x2 = 1.5 + -4x + 2x2 + -1.5 + 4x + -2x2

Reorder the terms:
-1.5 + 4x + -2x2 = 1.5 + -1.5 + -4x + 4x + 2x2 + -2x2

Combine like terms: 1.5 + -1.5 = 0.0
-1.5 + 4x + -2x2 = 0.0 + -4x + 4x + 2x2 + -2x2
-1.5 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
-1.5 + 4x + -2x2 = 0 + 2x2 + -2x2
-1.5 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1.5 + 4x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.75 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2x + x2 = 0 + -0.75
-2x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2x + x2 = -0.75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.75 + 1

Reorder the terms:
1 + -2x + x2 = -0.75 + 1

Combine like terms: -0.75 + 1 = 0.25
1 + -2x + x2 = 0.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(x + -1) equal to 0.5 and -0.5.

Subproblem 1

x + -1 = 0.5 Simplifying x + -1 = 0.5 Reorder the terms: -1 + x = 0.5 Solving -1 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.5 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.5 + 1 x = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 x = 1.5 Simplifying x = 1.5

Subproblem 2

x + -1 = -0.5 Simplifying x + -1 = -0.5 Reorder the terms: -1 + x = -0.5 Solving -1 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.5 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.5 + 1 x = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 x = 0.5 Simplifying x = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5, 0.5}

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