q^2-3q-13=0

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


Simplifying
q2 + -3q + -13 = 0

Reorder the terms:
-13 + -3q + q2 = 0

Solving
-13 + -3q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -3q + 13 + q2 = 0 + 13

Reorder the terms:
-13 + 13 + -3q + q2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3q + q2 = 0 + 13
-3q + q2 = 0 + 13

Combine like terms: 0 + 13 = 13
-3q + q2 = 13

The q term is -3q.  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.
-3q + 2.25 + q2 = 13 + 2.25

Reorder the terms:
2.25 + -3q + q2 = 13 + 2.25

Combine like terms: 13 + 2.25 = 15.25
2.25 + -3q + q2 = 15.25

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

Calculate the square root of the right side: 3.905124838

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

Subproblem 1

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

Subproblem 2

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

Solution

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

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