(a-2)(a-2)=9

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Solution for (a-2)(a-2)=9 equation:


Simplifying
(a + -2)(a + -2) = 9

Reorder the terms:
(-2 + a)(a + -2) = 9

Reorder the terms:
(-2 + a)(-2 + a) = 9

Multiply (-2 + a) * (-2 + a)
(-2(-2 + a) + a(-2 + a)) = 9
((-2 * -2 + a * -2) + a(-2 + a)) = 9
((4 + -2a) + a(-2 + a)) = 9
(4 + -2a + (-2 * a + a * a)) = 9
(4 + -2a + (-2a + a2)) = 9

Combine like terms: -2a + -2a = -4a
(4 + -4a + a2) = 9

Solving
4 + -4a + a2 = 9

Solving for variable 'a'.

Reorder the terms:
4 + -9 + -4a + a2 = 9 + -9

Combine like terms: 4 + -9 = -5
-5 + -4a + a2 = 9 + -9

Combine like terms: 9 + -9 = 0
-5 + -4a + a2 = 0

Factor a trinomial.
(-1 + -1a)(5 + -1a) = 0

Subproblem 1

Set the factor '(-1 + -1a)' equal to zero and attempt to solve: Simplifying -1 + -1a = 0 Solving -1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1a = 0 + 1 -1a = 0 + 1 Combine like terms: 0 + 1 = 1 -1a = 1 Divide each side by '-1'. a = -1 Simplifying a = -1

Subproblem 2

Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5

Solution

a = {-1, 5}

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