a^2-2a-12=0

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Solution for a^2-2a-12=0 equation:


Simplifying
a2 + -2a + -12 = 0

Reorder the terms:
-12 + -2a + a2 = 0

Solving
-12 + -2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -2a + 12 + a2 = 0 + 12

Reorder the terms:
-12 + 12 + -2a + a2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -2a + a2 = 0 + 12
-2a + a2 = 0 + 12

Combine like terms: 0 + 12 = 12
-2a + a2 = 12

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 = 12 + 1

Reorder the terms:
1 + -2a + a2 = 12 + 1

Combine like terms: 12 + 1 = 13
1 + -2a + a2 = 13

Factor a perfect square on the left side:
(a + -1)(a + -1) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(a + -1) equal to 3.605551275 and -3.605551275.

Subproblem 1

a + -1 = 3.605551275 Simplifying a + -1 = 3.605551275 Reorder the terms: -1 + a = 3.605551275 Solving -1 + a = 3.605551275 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 = 3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + a = 3.605551275 + 1 a = 3.605551275 + 1 Combine like terms: 3.605551275 + 1 = 4.605551275 a = 4.605551275 Simplifying a = 4.605551275

Subproblem 2

a + -1 = -3.605551275 Simplifying a + -1 = -3.605551275 Reorder the terms: -1 + a = -3.605551275 Solving -1 + a = -3.605551275 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 = -3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + a = -3.605551275 + 1 a = -3.605551275 + 1 Combine like terms: -3.605551275 + 1 = -2.605551275 a = -2.605551275 Simplifying a = -2.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.605551275, -2.605551275}

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