-5q^2+12q-2=0

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Solution for -5q^2+12q-2=0 equation:


Simplifying
-5q2 + 12q + -2 = 0

Reorder the terms:
-2 + 12q + -5q2 = 0

Solving
-2 + 12q + -5q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.4 + -2.4q + q2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2.4q + -0.4 + q2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2.4q + q2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2.4q + q2 = 0 + -0.4
-2.4q + q2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2.4q + q2 = -0.4

The q term is -2.4q.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4q + 1.44 + q2 = -0.4 + 1.44

Reorder the terms:
1.44 + -2.4q + q2 = -0.4 + 1.44

Combine like terms: -0.4 + 1.44 = 1.04
1.44 + -2.4q + q2 = 1.04

Factor a perfect square on the left side:
(q + -1.2)(q + -1.2) = 1.04

Calculate the square root of the right side: 1.019803903

Break this problem into two subproblems by setting 
(q + -1.2) equal to 1.019803903 and -1.019803903.

Subproblem 1

q + -1.2 = 1.019803903 Simplifying q + -1.2 = 1.019803903 Reorder the terms: -1.2 + q = 1.019803903 Solving -1.2 + q = 1.019803903 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + q = 1.019803903 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + q = 1.019803903 + 1.2 q = 1.019803903 + 1.2 Combine like terms: 1.019803903 + 1.2 = 2.219803903 q = 2.219803903 Simplifying q = 2.219803903

Subproblem 2

q + -1.2 = -1.019803903 Simplifying q + -1.2 = -1.019803903 Reorder the terms: -1.2 + q = -1.019803903 Solving -1.2 + q = -1.019803903 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + q = -1.019803903 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + q = -1.019803903 + 1.2 q = -1.019803903 + 1.2 Combine like terms: -1.019803903 + 1.2 = 0.180196097 q = 0.180196097 Simplifying q = 0.180196097

Solution

The solution to the problem is based on the solutions from the subproblems. q = {2.219803903, 0.180196097}

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