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Simplifying 900 + -16q + -1q2 = 0 Solving 900 + -16q + -1q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -900 + 16q + q2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + 16q + 900 + q2 = 0 + 900 Reorder the terms: -900 + 900 + 16q + q2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 16q + q2 = 0 + 900 16q + q2 = 0 + 900 Combine like terms: 0 + 900 = 900 16q + q2 = 900 The q term is 16q. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16q + 64 + q2 = 900 + 64 Reorder the terms: 64 + 16q + q2 = 900 + 64 Combine like terms: 900 + 64 = 964 64 + 16q + q2 = 964 Factor a perfect square on the left side: (q + 8)(q + 8) = 964 Calculate the square root of the right side: 31.048349393 Break this problem into two subproblems by setting (q + 8) equal to 31.048349393 and -31.048349393.Subproblem 1
q + 8 = 31.048349393 Simplifying q + 8 = 31.048349393 Reorder the terms: 8 + q = 31.048349393 Solving 8 + q = 31.048349393 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = 31.048349393 + -8 Combine like terms: 8 + -8 = 0 0 + q = 31.048349393 + -8 q = 31.048349393 + -8 Combine like terms: 31.048349393 + -8 = 23.048349393 q = 23.048349393 Simplifying q = 23.048349393Subproblem 2
q + 8 = -31.048349393 Simplifying q + 8 = -31.048349393 Reorder the terms: 8 + q = -31.048349393 Solving 8 + q = -31.048349393 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = -31.048349393 + -8 Combine like terms: 8 + -8 = 0 0 + q = -31.048349393 + -8 q = -31.048349393 + -8 Combine like terms: -31.048349393 + -8 = -39.048349393 q = -39.048349393 Simplifying q = -39.048349393Solution
The solution to the problem is based on the solutions from the subproblems. q = {23.048349393, -39.048349393}
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