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