2a^2+13a=20

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Solution for 2a^2+13a=20 equation:


Simplifying
2a2 + 13a = 20

Reorder the terms:
13a + 2a2 = 20

Solving
13a + 2a2 = 20

Solving for variable 'a'.

Reorder the terms:
-20 + 13a + 2a2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 13a + 2a2 = 0

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

Divide each side by '2'.
-10 + 6.5a + a2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6.5a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 6.5a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6.5a + a2 = 0 + 10
6.5a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
6.5a + a2 = 10

The a term is 6.5a.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5a + 10.5625 + a2 = 10 + 10.5625

Reorder the terms:
10.5625 + 6.5a + a2 = 10 + 10.5625

Combine like terms: 10 + 10.5625 = 20.5625
10.5625 + 6.5a + a2 = 20.5625

Factor a perfect square on the left side:
(a + 3.25)(a + 3.25) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(a + 3.25) equal to 4.534589287 and -4.534589287.

Subproblem 1

a + 3.25 = 4.534589287 Simplifying a + 3.25 = 4.534589287 Reorder the terms: 3.25 + a = 4.534589287 Solving 3.25 + a = 4.534589287 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + a = 4.534589287 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + a = 4.534589287 + -3.25 a = 4.534589287 + -3.25 Combine like terms: 4.534589287 + -3.25 = 1.284589287 a = 1.284589287 Simplifying a = 1.284589287

Subproblem 2

a + 3.25 = -4.534589287 Simplifying a + 3.25 = -4.534589287 Reorder the terms: 3.25 + a = -4.534589287 Solving 3.25 + a = -4.534589287 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + a = -4.534589287 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + a = -4.534589287 + -3.25 a = -4.534589287 + -3.25 Combine like terms: -4.534589287 + -3.25 = -7.784589287 a = -7.784589287 Simplifying a = -7.784589287

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.284589287, -7.784589287}

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