a^2+8a+13=0

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Solution for a^2+8a+13=0 equation:


Simplifying
a2 + 8a + 13 = 0

Reorder the terms:
13 + 8a + a2 = 0

Solving
13 + 8a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 8a + -13 + a2 = 0 + -13

Reorder the terms:
13 + -13 + 8a + a2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 8a + a2 = 0 + -13
8a + a2 = 0 + -13

Combine like terms: 0 + -13 = -13
8a + a2 = -13

The a term is 8a.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8a + 16 + a2 = -13 + 16

Reorder the terms:
16 + 8a + a2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + 8a + a2 = 3

Factor a perfect square on the left side:
(a + 4)(a + 4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + 4) equal to 1.732050808 and -1.732050808.

Subproblem 1

a + 4 = 1.732050808 Simplifying a + 4 = 1.732050808 Reorder the terms: 4 + a = 1.732050808 Solving 4 + a = 1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 1.732050808 + -4 Combine like terms: 4 + -4 = 0 0 + a = 1.732050808 + -4 a = 1.732050808 + -4 Combine like terms: 1.732050808 + -4 = -2.267949192 a = -2.267949192 Simplifying a = -2.267949192

Subproblem 2

a + 4 = -1.732050808 Simplifying a + 4 = -1.732050808 Reorder the terms: 4 + a = -1.732050808 Solving 4 + a = -1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = -1.732050808 + -4 Combine like terms: 4 + -4 = 0 0 + a = -1.732050808 + -4 a = -1.732050808 + -4 Combine like terms: -1.732050808 + -4 = -5.732050808 a = -5.732050808 Simplifying a = -5.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-2.267949192, -5.732050808}

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