a^2-a-13=0

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


Simplifying
a2 + -1a + -13 = 0

Reorder the terms:
-13 + -1a + a2 = 0

Solving
-13 + -1a + 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 + -1a + 13 + a2 = 0 + 13

Reorder the terms:
-13 + 13 + -1a + a2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1a + a2 = 0 + 13
-1a + a2 = 0 + 13

Combine like terms: 0 + 13 = 13
-1a + a2 = 13

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = 13 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 13 + 0.25

Combine like terms: 13 + 0.25 = 13.25
0.25 + -1a + a2 = 13.25

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(a + -0.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

a + -0.5 = 3.640054945 Simplifying a + -0.5 = 3.640054945 Reorder the terms: -0.5 + a = 3.640054945 Solving -0.5 + a = 3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 3.640054945 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 3.640054945 + 0.5 a = 3.640054945 + 0.5 Combine like terms: 3.640054945 + 0.5 = 4.140054945 a = 4.140054945 Simplifying a = 4.140054945

Subproblem 2

a + -0.5 = -3.640054945 Simplifying a + -0.5 = -3.640054945 Reorder the terms: -0.5 + a = -3.640054945 Solving -0.5 + a = -3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -3.640054945 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -3.640054945 + 0.5 a = -3.640054945 + 0.5 Combine like terms: -3.640054945 + 0.5 = -3.140054945 a = -3.140054945 Simplifying a = -3.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.140054945, -3.140054945}

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