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Simplifying 14 = 10 + 4q + 0.5q2 Solving 14 = 10 + 4q + 0.5q2 Solving for variable 'q'. Combine like terms: 14 + -10 = 4 4 + -4q + -0.5q2 = 10 + 4q + 0.5q2 + -10 + -4q + -0.5q2 Reorder the terms: 4 + -4q + -0.5q2 = 10 + -10 + 4q + -4q + 0.5q2 + -0.5q2 Combine like terms: 10 + -10 = 0 4 + -4q + -0.5q2 = 0 + 4q + -4q + 0.5q2 + -0.5q2 4 + -4q + -0.5q2 = 4q + -4q + 0.5q2 + -0.5q2 Combine like terms: 4q + -4q = 0 4 + -4q + -0.5q2 = 0 + 0.5q2 + -0.5q2 4 + -4q + -0.5q2 = 0.5q2 + -0.5q2 Combine like terms: 0.5q2 + -0.5q2 = 0.0 4 + -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'. -8 + 8q + q2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 8q + 8 + q2 = 0 + 8 Reorder the terms: -8 + 8 + 8q + q2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8q + q2 = 0 + 8 8q + q2 = 0 + 8 Combine like terms: 0 + 8 = 8 8q + q2 = 8 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 = 8 + 16 Reorder the terms: 16 + 8q + q2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + 8q + q2 = 24 Factor a perfect square on the left side: (q + 4)(q + 4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (q + 4) equal to 4.898979486 and -4.898979486.Subproblem 1
q + 4 = 4.898979486 Simplifying q + 4 = 4.898979486 Reorder the terms: 4 + q = 4.898979486 Solving 4 + q = 4.898979486 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 = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + q = 4.898979486 + -4 q = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 q = 0.898979486 Simplifying q = 0.898979486Subproblem 2
q + 4 = -4.898979486 Simplifying q + 4 = -4.898979486 Reorder the terms: 4 + q = -4.898979486 Solving 4 + q = -4.898979486 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 = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + q = -4.898979486 + -4 q = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 q = -8.898979486 Simplifying q = -8.898979486Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.898979486, -8.898979486}
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