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Simplifying -3q2 + -6q + 299 = 0 Reorder the terms: 299 + -6q + -3q2 = 0 Solving 299 + -6q + -3q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -99.66666667 + 2q + q2 = 0 Move the constant term to the right: Add '99.66666667' to each side of the equation. -99.66666667 + 2q + 99.66666667 + q2 = 0 + 99.66666667 Reorder the terms: -99.66666667 + 99.66666667 + 2q + q2 = 0 + 99.66666667 Combine like terms: -99.66666667 + 99.66666667 = 0.00000000 0.00000000 + 2q + q2 = 0 + 99.66666667 2q + q2 = 0 + 99.66666667 Combine like terms: 0 + 99.66666667 = 99.66666667 2q + q2 = 99.66666667 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = 99.66666667 + 1 Reorder the terms: 1 + 2q + q2 = 99.66666667 + 1 Combine like terms: 99.66666667 + 1 = 100.66666667 1 + 2q + q2 = 100.66666667 Factor a perfect square on the left side: (q + 1)(q + 1) = 100.66666667 Calculate the square root of the right side: 10.033277962 Break this problem into two subproblems by setting (q + 1) equal to 10.033277962 and -10.033277962.Subproblem 1
q + 1 = 10.033277962 Simplifying q + 1 = 10.033277962 Reorder the terms: 1 + q = 10.033277962 Solving 1 + q = 10.033277962 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 10.033277962 + -1 Combine like terms: 1 + -1 = 0 0 + q = 10.033277962 + -1 q = 10.033277962 + -1 Combine like terms: 10.033277962 + -1 = 9.033277962 q = 9.033277962 Simplifying q = 9.033277962Subproblem 2
q + 1 = -10.033277962 Simplifying q + 1 = -10.033277962 Reorder the terms: 1 + q = -10.033277962 Solving 1 + q = -10.033277962 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -10.033277962 + -1 Combine like terms: 1 + -1 = 0 0 + q = -10.033277962 + -1 q = -10.033277962 + -1 Combine like terms: -10.033277962 + -1 = -11.033277962 q = -11.033277962 Simplifying q = -11.033277962Solution
The solution to the problem is based on the solutions from the subproblems. q = {9.033277962, -11.033277962}
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