2a^2-a-13=12

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


Simplifying
2a2 + -1a + -13 = 12

Reorder the terms:
-13 + -1a + 2a2 = 12

Solving
-13 + -1a + 2a2 = 12

Solving for variable 'a'.

Reorder the terms:
-13 + -12 + -1a + 2a2 = 12 + -12

Combine like terms: -13 + -12 = -25
-25 + -1a + 2a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-25 + -1a + 2a2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-12.5 + -0.5a + a2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -0.5a + 12.5 + a2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -0.5a + a2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -0.5a + a2 = 0 + 12.5
-0.5a + a2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-0.5a + a2 = 12.5

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = 12.5 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = 12.5 + 0.0625

Combine like terms: 12.5 + 0.0625 = 12.5625
0.0625 + -0.5a + a2 = 12.5625

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(a + -0.25) equal to 3.54436172 and -3.54436172.

Subproblem 1

a + -0.25 = 3.54436172 Simplifying a + -0.25 = 3.54436172 Reorder the terms: -0.25 + a = 3.54436172 Solving -0.25 + a = 3.54436172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 3.54436172 + 0.25 a = 3.54436172 + 0.25 Combine like terms: 3.54436172 + 0.25 = 3.79436172 a = 3.79436172 Simplifying a = 3.79436172

Subproblem 2

a + -0.25 = -3.54436172 Simplifying a + -0.25 = -3.54436172 Reorder the terms: -0.25 + a = -3.54436172 Solving -0.25 + a = -3.54436172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -3.54436172 + 0.25 a = -3.54436172 + 0.25 Combine like terms: -3.54436172 + 0.25 = -3.29436172 a = -3.29436172 Simplifying a = -3.29436172

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.79436172, -3.29436172}

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