a^2=2a+6

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Solution for a^2=2a+6 equation:


Simplifying
a2 = 2a + 6

Reorder the terms:
a2 = 6 + 2a

Solving
a2 = 6 + 2a

Solving for variable 'a'.

Reorder the terms:
-6 + -2a + a2 = 6 + 2a + -6 + -2a

Reorder the terms:
-6 + -2a + a2 = 6 + -6 + 2a + -2a

Combine like terms: 6 + -6 = 0
-6 + -2a + a2 = 0 + 2a + -2a
-6 + -2a + a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-6 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + -2a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2a + a2 = 0 + 6
-2a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2a + a2 = 6

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 = 6 + 1

Reorder the terms:
1 + -2a + a2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2a + a2 = 7

Factor a perfect square on the left side:
(a + -1)(a + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(a + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1

a + -1 = 2.645751311 Simplifying a + -1 = 2.645751311 Reorder the terms: -1 + a = 2.645751311 Solving -1 + a = 2.645751311 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 = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.645751311 + 1 a = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 a = 3.645751311 Simplifying a = 3.645751311

Subproblem 2

a + -1 = -2.645751311 Simplifying a + -1 = -2.645751311 Reorder the terms: -1 + a = -2.645751311 Solving -1 + a = -2.645751311 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 = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.645751311 + 1 a = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 a = -1.645751311 Simplifying a = -1.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.645751311, -1.645751311}

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