(2x-3)(x-2)=4

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Solution for (2x-3)(x-2)=4 equation:


Simplifying
(2x + -3)(x + -2) = 4

Reorder the terms:
(-3 + 2x)(x + -2) = 4

Reorder the terms:
(-3 + 2x)(-2 + x) = 4

Multiply (-3 + 2x) * (-2 + x)
(-3(-2 + x) + 2x * (-2 + x)) = 4
((-2 * -3 + x * -3) + 2x * (-2 + x)) = 4
((6 + -3x) + 2x * (-2 + x)) = 4
(6 + -3x + (-2 * 2x + x * 2x)) = 4
(6 + -3x + (-4x + 2x2)) = 4

Combine like terms: -3x + -4x = -7x
(6 + -7x + 2x2) = 4

Solving
6 + -7x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
6 + -4 + -7x + 2x2 = 4 + -4

Combine like terms: 6 + -4 = 2
2 + -7x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
2 + -7x + 2x2 = 0

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

Divide each side by '2'.
1 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.5x + x2 = 0 + -1
-3.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.5x + x2 = -1

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -1 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -1 + 3.0625

Combine like terms: -1 + 3.0625 = 2.0625
3.0625 + -3.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.436140662 and -1.436140662.

Subproblem 1

x + -1.75 = 1.436140662 Simplifying x + -1.75 = 1.436140662 Reorder the terms: -1.75 + x = 1.436140662 Solving -1.75 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.436140662 + 1.75 x = 1.436140662 + 1.75 Combine like terms: 1.436140662 + 1.75 = 3.186140662 x = 3.186140662 Simplifying x = 3.186140662

Subproblem 2

x + -1.75 = -1.436140662 Simplifying x + -1.75 = -1.436140662 Reorder the terms: -1.75 + x = -1.436140662 Solving -1.75 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.436140662 + 1.75 x = -1.436140662 + 1.75 Combine like terms: -1.436140662 + 1.75 = 0.313859338 x = 0.313859338 Simplifying x = 0.313859338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.186140662, 0.313859338}

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