q^2+12q-20=0

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Solution for q^2+12q-20=0 equation:


Simplifying
q2 + 12q + -20 = 0

Reorder the terms:
-20 + 12q + q2 = 0

Solving
-20 + 12q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 12q + 20 + q2 = 0 + 20

Reorder the terms:
-20 + 20 + 12q + q2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 12q + q2 = 0 + 20
12q + q2 = 0 + 20

Combine like terms: 0 + 20 = 20
12q + q2 = 20

The q term is 12q.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12q + 36 + q2 = 20 + 36

Reorder the terms:
36 + 12q + q2 = 20 + 36

Combine like terms: 20 + 36 = 56
36 + 12q + q2 = 56

Factor a perfect square on the left side:
(q + 6)(q + 6) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(q + 6) equal to 7.483314774 and -7.483314774.

Subproblem 1

q + 6 = 7.483314774 Simplifying q + 6 = 7.483314774 Reorder the terms: 6 + q = 7.483314774 Solving 6 + q = 7.483314774 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + q = 7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + q = 7.483314774 + -6 q = 7.483314774 + -6 Combine like terms: 7.483314774 + -6 = 1.483314774 q = 1.483314774 Simplifying q = 1.483314774

Subproblem 2

q + 6 = -7.483314774 Simplifying q + 6 = -7.483314774 Reorder the terms: 6 + q = -7.483314774 Solving 6 + q = -7.483314774 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + q = -7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + q = -7.483314774 + -6 q = -7.483314774 + -6 Combine like terms: -7.483314774 + -6 = -13.483314774 q = -13.483314774 Simplifying q = -13.483314774

Solution

The solution to the problem is based on the solutions from the subproblems. q = {1.483314774, -13.483314774}

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