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Simplifying 9q2 + -71q + -36 = 0 Reorder the terms: -36 + -71q + 9q2 = 0 Solving -36 + -71q + 9q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4 + -7.888888889q + q2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -7.888888889q + 4 + q2 = 0 + 4 Reorder the terms: -4 + 4 + -7.888888889q + q2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7.888888889q + q2 = 0 + 4 -7.888888889q + q2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7.888888889q + q2 = 4 The q term is -7.888888889q. Take half its coefficient (-3.944444445). Square it (15.55864198) and add it to both sides. Add '15.55864198' to each side of the equation. -7.888888889q + 15.55864198 + q2 = 4 + 15.55864198 Reorder the terms: 15.55864198 + -7.888888889q + q2 = 4 + 15.55864198 Combine like terms: 4 + 15.55864198 = 19.55864198 15.55864198 + -7.888888889q + q2 = 19.55864198 Factor a perfect square on the left side: (q + -3.944444445)(q + -3.944444445) = 19.55864198 Calculate the square root of the right side: 4.422515345 Break this problem into two subproblems by setting (q + -3.944444445) equal to 4.422515345 and -4.422515345.Subproblem 1
q + -3.944444445 = 4.422515345 Simplifying q + -3.944444445 = 4.422515345 Reorder the terms: -3.944444445 + q = 4.422515345 Solving -3.944444445 + q = 4.422515345 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.944444445' to each side of the equation. -3.944444445 + 3.944444445 + q = 4.422515345 + 3.944444445 Combine like terms: -3.944444445 + 3.944444445 = 0.000000000 0.000000000 + q = 4.422515345 + 3.944444445 q = 4.422515345 + 3.944444445 Combine like terms: 4.422515345 + 3.944444445 = 8.36695979 q = 8.36695979 Simplifying q = 8.36695979Subproblem 2
q + -3.944444445 = -4.422515345 Simplifying q + -3.944444445 = -4.422515345 Reorder the terms: -3.944444445 + q = -4.422515345 Solving -3.944444445 + q = -4.422515345 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.944444445' to each side of the equation. -3.944444445 + 3.944444445 + q = -4.422515345 + 3.944444445 Combine like terms: -3.944444445 + 3.944444445 = 0.000000000 0.000000000 + q = -4.422515345 + 3.944444445 q = -4.422515345 + 3.944444445 Combine like terms: -4.422515345 + 3.944444445 = -0.4780709 q = -0.4780709 Simplifying q = -0.4780709Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.36695979, -0.4780709}
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