(2x-3)(x-0.5)=0

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Solution for (2x-3)(x-0.5)=0 equation:


Simplifying
(2x + -3)(x + -0.5) = 0

Reorder the terms:
(-3 + 2x)(x + -0.5) = 0

Reorder the terms:
(-3 + 2x)(-0.5 + x) = 0

Multiply (-3 + 2x) * (-0.5 + x)
(-3(-0.5 + x) + 2x * (-0.5 + x)) = 0
((-0.5 * -3 + x * -3) + 2x * (-0.5 + x)) = 0
((1.5 + -3x) + 2x * (-0.5 + x)) = 0
(1.5 + -3x + (-0.5 * 2x + x * 2x)) = 0
(1.5 + -3x + (-1x + 2x2)) = 0

Combine like terms: -3x + -1x = -4x
(1.5 + -4x + 2x2) = 0

Solving
1.5 + -4x + 2x2 = 0

Solving for variable 'x'.

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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