a^2-3a-13=0

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Solution for a^2-3a-13=0 equation:


Simplifying
a2 + -3a + -13 = 0

Reorder the terms:
-13 + -3a + a2 = 0

Solving
-13 + -3a + 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 + -3a + 13 + a2 = 0 + 13

Reorder the terms:
-13 + 13 + -3a + a2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3a + a2 = 0 + 13
-3a + a2 = 0 + 13

Combine like terms: 0 + 13 = 13
-3a + a2 = 13

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = 13 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 13 + 2.25

Combine like terms: 13 + 2.25 = 15.25
2.25 + -3a + a2 = 15.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(a + -1.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

a + -1.5 = 3.905124838 Simplifying a + -1.5 = 3.905124838 Reorder the terms: -1.5 + a = 3.905124838 Solving -1.5 + a = 3.905124838 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 3.905124838 + 1.5 a = 3.905124838 + 1.5 Combine like terms: 3.905124838 + 1.5 = 5.405124838 a = 5.405124838 Simplifying a = 5.405124838

Subproblem 2

a + -1.5 = -3.905124838 Simplifying a + -1.5 = -3.905124838 Reorder the terms: -1.5 + a = -3.905124838 Solving -1.5 + a = -3.905124838 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -3.905124838 + 1.5 a = -3.905124838 + 1.5 Combine like terms: -3.905124838 + 1.5 = -2.405124838 a = -2.405124838 Simplifying a = -2.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.405124838, -2.405124838}

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