a^2-6a-13=0

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Solution for a^2-6a-13=0 equation:


Simplifying
a2 + -6a + -13 = 0

Reorder the terms:
-13 + -6a + a2 = 0

Solving
-13 + -6a + 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 + -6a + 13 + a2 = 0 + 13

Reorder the terms:
-13 + 13 + -6a + a2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6a + a2 = 0 + 13
-6a + a2 = 0 + 13

Combine like terms: 0 + 13 = 13
-6a + a2 = 13

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = 13 + 9

Reorder the terms:
9 + -6a + a2 = 13 + 9

Combine like terms: 13 + 9 = 22
9 + -6a + a2 = 22

Factor a perfect square on the left side:
(a + -3)(a + -3) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(a + -3) equal to 4.69041576 and -4.69041576.

Subproblem 1

a + -3 = 4.69041576 Simplifying a + -3 = 4.69041576 Reorder the terms: -3 + a = 4.69041576 Solving -3 + a = 4.69041576 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + a = 4.69041576 + 3 a = 4.69041576 + 3 Combine like terms: 4.69041576 + 3 = 7.69041576 a = 7.69041576 Simplifying a = 7.69041576

Subproblem 2

a + -3 = -4.69041576 Simplifying a + -3 = -4.69041576 Reorder the terms: -3 + a = -4.69041576 Solving -3 + a = -4.69041576 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + a = -4.69041576 + 3 a = -4.69041576 + 3 Combine like terms: -4.69041576 + 3 = -1.69041576 a = -1.69041576 Simplifying a = -1.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. a = {7.69041576, -1.69041576}

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