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

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


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

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

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

Multiply (3 + a) * (-3 + a)
(3(-3 + a) + a(-3 + a)) = 2a
((-3 * 3 + a * 3) + a(-3 + a)) = 2a
((-9 + 3a) + a(-3 + a)) = 2a
(-9 + 3a + (-3 * a + a * a)) = 2a
(-9 + 3a + (-3a + a2)) = 2a

Combine like terms: 3a + -3a = 0
(-9 + 0 + a2) = 2a
(-9 + a2) = 2a

Solving
-9 + a2 = 2a

Solving for variable 'a'.

Reorder the terms:
-9 + -2a + a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-9 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + -2a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2a + a2 = 0 + 9
-2a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2a + a2 = 9

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

Add '1' to each side of the equation.
-2a + 1 + a2 = 9 + 1

Reorder the terms:
1 + -2a + a2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2a + a2 = 10

Factor a perfect square on the left side:
(a + -1)(a + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(a + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1

a + -1 = 3.16227766 Simplifying a + -1 = 3.16227766 Reorder the terms: -1 + a = 3.16227766 Solving -1 + a = 3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + a = 3.16227766 + 1 a = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 a = 4.16227766 Simplifying a = 4.16227766

Subproblem 2

a + -1 = -3.16227766 Simplifying a + -1 = -3.16227766 Reorder the terms: -1 + a = -3.16227766 Solving -1 + a = -3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + a = -3.16227766 + 1 a = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 a = -2.16227766 Simplifying a = -2.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.16227766, -2.16227766}

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