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Simplifying 0 = q2 + 25q + -100 Reorder the terms: 0 = -100 + 25q + q2 Solving 0 = -100 + 25q + q2 Solving for variable 'q'. Combine like terms: 0 + 100 = 100 100 + -25q + -1q2 = -100 + 25q + q2 + 100 + -25q + -1q2 Reorder the terms: 100 + -25q + -1q2 = -100 + 100 + 25q + -25q + q2 + -1q2 Combine like terms: -100 + 100 = 0 100 + -25q + -1q2 = 0 + 25q + -25q + q2 + -1q2 100 + -25q + -1q2 = 25q + -25q + q2 + -1q2 Combine like terms: 25q + -25q = 0 100 + -25q + -1q2 = 0 + q2 + -1q2 100 + -25q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 100 + -25q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 25q + q2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 25q + 100 + q2 = 0 + 100 Reorder the terms: -100 + 100 + 25q + q2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 25q + q2 = 0 + 100 25q + q2 = 0 + 100 Combine like terms: 0 + 100 = 100 25q + q2 = 100 The q term is 25q. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25q + 156.25 + q2 = 100 + 156.25 Reorder the terms: 156.25 + 25q + q2 = 100 + 156.25 Combine like terms: 100 + 156.25 = 256.25 156.25 + 25q + q2 = 256.25 Factor a perfect square on the left side: (q + 12.5)(q + 12.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (q + 12.5) equal to 16.007810594 and -16.007810594.Subproblem 1
q + 12.5 = 16.007810594 Simplifying q + 12.5 = 16.007810594 Reorder the terms: 12.5 + q = 16.007810594 Solving 12.5 + q = 16.007810594 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + q = 16.007810594 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + q = 16.007810594 + -12.5 q = 16.007810594 + -12.5 Combine like terms: 16.007810594 + -12.5 = 3.507810594 q = 3.507810594 Simplifying q = 3.507810594Subproblem 2
q + 12.5 = -16.007810594 Simplifying q + 12.5 = -16.007810594 Reorder the terms: 12.5 + q = -16.007810594 Solving 12.5 + q = -16.007810594 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + q = -16.007810594 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + q = -16.007810594 + -12.5 q = -16.007810594 + -12.5 Combine like terms: -16.007810594 + -12.5 = -28.507810594 q = -28.507810594 Simplifying q = -28.507810594Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.507810594, -28.507810594}
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