86.5+-1q+-1.5q^2-2q^2+3q+71=0

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Solution for 86.5+-1q+-1.5q^2-2q^2+3q+71=0 equation:


Simplifying
86.5 + -1q + -1.5q2 + -2q2 + 3q + 71 = 0

Reorder the terms:
86.5 + 71 + -1q + 3q + -1.5q2 + -2q2 = 0

Combine like terms: 86.5 + 71 = 157.5
157.5 + -1q + 3q + -1.5q2 + -2q2 = 0

Combine like terms: -1q + 3q = 2q
157.5 + 2q + -1.5q2 + -2q2 = 0

Combine like terms: -1.5q2 + -2q2 = -3.5q2
157.5 + 2q + -3.5q2 = 0

Solving
157.5 + 2q + -3.5q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
-3.5 the coefficient of the squared term: 

Divide each side by '-3.5'.
-45 + -0.5714285714q + q2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -0.5714285714q + 45 + q2 = 0 + 45

Reorder the terms:
-45 + 45 + -0.5714285714q + q2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -0.5714285714q + q2 = 0 + 45
-0.5714285714q + q2 = 0 + 45

Combine like terms: 0 + 45 = 45
-0.5714285714q + q2 = 45

The q term is -0.5714285714q.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714q + 0.08163265305 + q2 = 45 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714q + q2 = 45 + 0.08163265305

Combine like terms: 45 + 0.08163265305 = 45.08163265305
0.08163265305 + -0.5714285714q + q2 = 45.08163265305

Factor a perfect square on the left side:
(q + -0.2857142857)(q + -0.2857142857) = 45.08163265305

Calculate the square root of the right side: 6.714285714

Break this problem into two subproblems by setting 
(q + -0.2857142857) equal to 6.714285714 and -6.714285714.

Subproblem 1

q + -0.2857142857 = 6.714285714 Simplifying q + -0.2857142857 = 6.714285714 Reorder the terms: -0.2857142857 + q = 6.714285714 Solving -0.2857142857 + q = 6.714285714 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + q = 6.714285714 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + q = 6.714285714 + 0.2857142857 q = 6.714285714 + 0.2857142857 Combine like terms: 6.714285714 + 0.2857142857 = 6.9999999997 q = 6.9999999997 Simplifying q = 6.9999999997

Subproblem 2

q + -0.2857142857 = -6.714285714 Simplifying q + -0.2857142857 = -6.714285714 Reorder the terms: -0.2857142857 + q = -6.714285714 Solving -0.2857142857 + q = -6.714285714 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + q = -6.714285714 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + q = -6.714285714 + 0.2857142857 q = -6.714285714 + 0.2857142857 Combine like terms: -6.714285714 + 0.2857142857 = -6.4285714283 q = -6.4285714283 Simplifying q = -6.4285714283

Solution

The solution to the problem is based on the solutions from the subproblems. q = {6.9999999997, -6.4285714283}

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