a^2+13a=12

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Solution for a^2+13a=12 equation:


Simplifying
a2 + 13a = 12

Reorder the terms:
13a + a2 = 12

Solving
13a + a2 = 12

Solving for variable 'a'.

Reorder the terms:
-12 + 13a + a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 13a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 13a + 12 + a2 = 0 + 12

Reorder the terms:
-12 + 12 + 13a + a2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 13a + a2 = 0 + 12
13a + a2 = 0 + 12

Combine like terms: 0 + 12 = 12
13a + a2 = 12

The a term is 13a.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13a + 42.25 + a2 = 12 + 42.25

Reorder the terms:
42.25 + 13a + a2 = 12 + 42.25

Combine like terms: 12 + 42.25 = 54.25
42.25 + 13a + a2 = 54.25

Factor a perfect square on the left side:
(a + 6.5)(a + 6.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(a + 6.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

a + 6.5 = 7.365459931 Simplifying a + 6.5 = 7.365459931 Reorder the terms: 6.5 + a = 7.365459931 Solving 6.5 + a = 7.365459931 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 7.365459931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 7.365459931 + -6.5 a = 7.365459931 + -6.5 Combine like terms: 7.365459931 + -6.5 = 0.865459931 a = 0.865459931 Simplifying a = 0.865459931

Subproblem 2

a + 6.5 = -7.365459931 Simplifying a + 6.5 = -7.365459931 Reorder the terms: 6.5 + a = -7.365459931 Solving 6.5 + a = -7.365459931 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -7.365459931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -7.365459931 + -6.5 a = -7.365459931 + -6.5 Combine like terms: -7.365459931 + -6.5 = -13.865459931 a = -13.865459931 Simplifying a = -13.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.865459931, -13.865459931}

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