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Simplifying 14 = 4q + 0.5q2 Solving 14 = 4q + 0.5q2 Solving for variable 'q'. Reorder the terms: 14 + -4q + -0.5q2 = 4q + -4q + 0.5q2 + -0.5q2 Combine like terms: 4q + -4q = 0 14 + -4q + -0.5q2 = 0 + 0.5q2 + -0.5q2 14 + -4q + -0.5q2 = 0.5q2 + -0.5q2 Combine like terms: 0.5q2 + -0.5q2 = 0.0 14 + -4q + -0.5q2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -28 + 8q + q2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 8q + 28 + q2 = 0 + 28 Reorder the terms: -28 + 28 + 8q + q2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 8q + q2 = 0 + 28 8q + q2 = 0 + 28 Combine like terms: 0 + 28 = 28 8q + q2 = 28 The q term is 8q. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8q + 16 + q2 = 28 + 16 Reorder the terms: 16 + 8q + q2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + 8q + q2 = 44 Factor a perfect square on the left side: (q + 4)(q + 4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (q + 4) equal to 6.633249581 and -6.633249581.Subproblem 1
q + 4 = 6.633249581 Simplifying q + 4 = 6.633249581 Reorder the terms: 4 + q = 6.633249581 Solving 4 + q = 6.633249581 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = 6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + q = 6.633249581 + -4 q = 6.633249581 + -4 Combine like terms: 6.633249581 + -4 = 2.633249581 q = 2.633249581 Simplifying q = 2.633249581Subproblem 2
q + 4 = -6.633249581 Simplifying q + 4 = -6.633249581 Reorder the terms: 4 + q = -6.633249581 Solving 4 + q = -6.633249581 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = -6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + q = -6.633249581 + -4 q = -6.633249581 + -4 Combine like terms: -6.633249581 + -4 = -10.633249581 q = -10.633249581 Simplifying q = -10.633249581Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.633249581, -10.633249581}
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