-0.12q^2+1.8q-6=0

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Solution for -0.12q^2+1.8q-6=0 equation:


Simplifying
-0.12q2 + 1.8q + -6 = 0

Reorder the terms:
-6 + 1.8q + -0.12q2 = 0

Solving
-6 + 1.8q + -0.12q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
-0.12 the coefficient of the squared term: 

Divide each side by '-0.12'.
50 + -15q + q2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -15q + -50 + q2 = 0 + -50

Reorder the terms:
50 + -50 + -15q + q2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -15q + q2 = 0 + -50
-15q + q2 = 0 + -50

Combine like terms: 0 + -50 = -50
-15q + q2 = -50

The q term is -15q.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15q + 56.25 + q2 = -50 + 56.25

Reorder the terms:
56.25 + -15q + q2 = -50 + 56.25

Combine like terms: -50 + 56.25 = 6.25
56.25 + -15q + q2 = 6.25

Factor a perfect square on the left side:
(q + -7.5)(q + -7.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(q + -7.5) equal to 2.5 and -2.5.

Subproblem 1

q + -7.5 = 2.5 Simplifying q + -7.5 = 2.5 Reorder the terms: -7.5 + q = 2.5 Solving -7.5 + q = 2.5 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = 2.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = 2.5 + 7.5 q = 2.5 + 7.5 Combine like terms: 2.5 + 7.5 = 10 q = 10 Simplifying q = 10

Subproblem 2

q + -7.5 = -2.5 Simplifying q + -7.5 = -2.5 Reorder the terms: -7.5 + q = -2.5 Solving -7.5 + q = -2.5 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = -2.5 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = -2.5 + 7.5 q = -2.5 + 7.5 Combine like terms: -2.5 + 7.5 = 5 q = 5 Simplifying q = 5

Solution

The solution to the problem is based on the solutions from the subproblems. q = {10, 5}

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