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Simplifying 24q + 3q2 = 63 Solving 24q + 3q2 = 63 Solving for variable 'q'. Reorder the terms: -63 + 24q + 3q2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 24q + 3q2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + 8q + q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-21 + 8q + q2)' equal to zero and attempt to solve: Simplifying -21 + 8q + q2 = 0 Solving -21 + 8q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 8q + 21 + q2 = 0 + 21 Reorder the terms: -21 + 21 + 8q + q2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8q + q2 = 0 + 21 8q + q2 = 0 + 21 Combine like terms: 0 + 21 = 21 8q + q2 = 21 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 = 21 + 16 Reorder the terms: 16 + 8q + q2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + 8q + q2 = 37 Factor a perfect square on the left side: (q + 4)(q + 4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (q + 4) equal to 6.08276253 and -6.08276253.Subproblem 1
q + 4 = 6.08276253 Simplifying q + 4 = 6.08276253 Reorder the terms: 4 + q = 6.08276253 Solving 4 + q = 6.08276253 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 = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + q = 6.08276253 + -4 q = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 q = 2.08276253 Simplifying q = 2.08276253Subproblem 2
q + 4 = -6.08276253 Simplifying q + 4 = -6.08276253 Reorder the terms: 4 + q = -6.08276253 Solving 4 + q = -6.08276253 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 = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + q = -6.08276253 + -4 q = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 q = -10.08276253 Simplifying q = -10.08276253Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.08276253, -10.08276253}Solution
q = {2.08276253, -10.08276253}
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