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Simplifying 5q2 + -6q = 4q + -8q + 63 Reorder the terms: -6q + 5q2 = 4q + -8q + 63 Reorder the terms: -6q + 5q2 = 63 + 4q + -8q Combine like terms: 4q + -8q = -4q -6q + 5q2 = 63 + -4q Solving -6q + 5q2 = 63 + -4q Solving for variable 'q'. Reorder the terms: -63 + -6q + 4q + 5q2 = 63 + -4q + -63 + 4q Combine like terms: -6q + 4q = -2q -63 + -2q + 5q2 = 63 + -4q + -63 + 4q Reorder the terms: -63 + -2q + 5q2 = 63 + -63 + -4q + 4q Combine like terms: 63 + -63 = 0 -63 + -2q + 5q2 = 0 + -4q + 4q -63 + -2q + 5q2 = -4q + 4q Combine like terms: -4q + 4q = 0 -63 + -2q + 5q2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + -0.4q + q2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + -0.4q + 12.6 + q2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + -0.4q + q2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + -0.4q + q2 = 0 + 12.6 -0.4q + q2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 -0.4q + q2 = 12.6 The q term is -0.4q. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4q + 0.04 + q2 = 12.6 + 0.04 Reorder the terms: 0.04 + -0.4q + q2 = 12.6 + 0.04 Combine like terms: 12.6 + 0.04 = 12.64 0.04 + -0.4q + q2 = 12.64 Factor a perfect square on the left side: (q + -0.2)(q + -0.2) = 12.64 Calculate the square root of the right side: 3.555277767 Break this problem into two subproblems by setting (q + -0.2) equal to 3.555277767 and -3.555277767.Subproblem 1
q + -0.2 = 3.555277767 Simplifying q + -0.2 = 3.555277767 Reorder the terms: -0.2 + q = 3.555277767 Solving -0.2 + q = 3.555277767 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + q = 3.555277767 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + q = 3.555277767 + 0.2 q = 3.555277767 + 0.2 Combine like terms: 3.555277767 + 0.2 = 3.755277767 q = 3.755277767 Simplifying q = 3.755277767Subproblem 2
q + -0.2 = -3.555277767 Simplifying q + -0.2 = -3.555277767 Reorder the terms: -0.2 + q = -3.555277767 Solving -0.2 + q = -3.555277767 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + q = -3.555277767 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + q = -3.555277767 + 0.2 q = -3.555277767 + 0.2 Combine like terms: -3.555277767 + 0.2 = -3.355277767 q = -3.355277767 Simplifying q = -3.355277767Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.755277767, -3.355277767}
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