(a-3)(a-2)=4

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


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

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

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

Multiply (-3 + a) * (-2 + a)
(-3(-2 + a) + a(-2 + a)) = 4
((-2 * -3 + a * -3) + a(-2 + a)) = 4
((6 + -3a) + a(-2 + a)) = 4
(6 + -3a + (-2 * a + a * a)) = 4
(6 + -3a + (-2a + a2)) = 4

Combine like terms: -3a + -2a = -5a
(6 + -5a + a2) = 4

Solving
6 + -5a + a2 = 4

Solving for variable 'a'.

Reorder the terms:
6 + -4 + -5a + a2 = 4 + -4

Combine like terms: 6 + -4 = 2
2 + -5a + a2 = 4 + -4

Combine like terms: 4 + -4 = 0
2 + -5a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -5a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + -5a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a + a2 = 0 + -2
-5a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-5a + a2 = -2

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = -2 + 6.25

Reorder the terms:
6.25 + -5a + a2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5a + a2 = 4.25

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(a + -2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

a + -2.5 = 2.061552813 Simplifying a + -2.5 = 2.061552813 Reorder the terms: -2.5 + a = 2.061552813 Solving -2.5 + a = 2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 2.061552813 + 2.5 a = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 a = 4.561552813 Simplifying a = 4.561552813

Subproblem 2

a + -2.5 = -2.061552813 Simplifying a + -2.5 = -2.061552813 Reorder the terms: -2.5 + a = -2.061552813 Solving -2.5 + a = -2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -2.061552813 + 2.5 a = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 a = 0.438447187 Simplifying a = 0.438447187

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.561552813, 0.438447187}

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