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Simplifying -6 = -9q2 + 5q Reorder the terms: -6 = 5q + -9q2 Solving -6 = 5q + -9q2 Solving for variable 'q'. Reorder the terms: -6 + -5q + 9q2 = 5q + -5q + -9q2 + 9q2 Combine like terms: 5q + -5q = 0 -6 + -5q + 9q2 = 0 + -9q2 + 9q2 -6 + -5q + 9q2 = -9q2 + 9q2 Combine like terms: -9q2 + 9q2 = 0 -6 + -5q + 9q2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + -0.5555555556q + q2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.5555555556q + 0.6666666667 + q2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.5555555556q + q2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.5555555556q + q2 = 0 + 0.6666666667 -0.5555555556q + q2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.5555555556q + q2 = 0.6666666667 The q term is -0.5555555556q. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556q + 0.07716049384 + q2 = 0.6666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556q + q2 = 0.6666666667 + 0.07716049384 Combine like terms: 0.6666666667 + 0.07716049384 = 0.74382716054 0.07716049384 + -0.5555555556q + q2 = 0.74382716054 Factor a perfect square on the left side: (q + -0.2777777778)(q + -0.2777777778) = 0.74382716054 Calculate the square root of the right side: 0.86245415 Break this problem into two subproblems by setting (q + -0.2777777778) equal to 0.86245415 and -0.86245415.Subproblem 1
q + -0.2777777778 = 0.86245415 Simplifying q + -0.2777777778 = 0.86245415 Reorder the terms: -0.2777777778 + q = 0.86245415 Solving -0.2777777778 + q = 0.86245415 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + q = 0.86245415 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + q = 0.86245415 + 0.2777777778 q = 0.86245415 + 0.2777777778 Combine like terms: 0.86245415 + 0.2777777778 = 1.1402319278 q = 1.1402319278 Simplifying q = 1.1402319278Subproblem 2
q + -0.2777777778 = -0.86245415 Simplifying q + -0.2777777778 = -0.86245415 Reorder the terms: -0.2777777778 + q = -0.86245415 Solving -0.2777777778 + q = -0.86245415 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + q = -0.86245415 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + q = -0.86245415 + 0.2777777778 q = -0.86245415 + 0.2777777778 Combine like terms: -0.86245415 + 0.2777777778 = -0.5846763722 q = -0.5846763722 Simplifying q = -0.5846763722Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.1402319278, -0.5846763722}
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