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Simplifying 3q2 + -36q + 75 = 0 Reorder the terms: 75 + -36q + 3q2 = 0 Solving 75 + -36q + 3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -12q + q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(25 + -12q + q2)' equal to zero and attempt to solve: Simplifying 25 + -12q + q2 = 0 Solving 25 + -12q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -12q + -25 + q2 = 0 + -25 Reorder the terms: 25 + -25 + -12q + q2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -12q + q2 = 0 + -25 -12q + q2 = 0 + -25 Combine like terms: 0 + -25 = -25 -12q + q2 = -25 The q term is -12q. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12q + 36 + q2 = -25 + 36 Reorder the terms: 36 + -12q + q2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + -12q + q2 = 11 Factor a perfect square on the left side: (q + -6)(q + -6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (q + -6) equal to 3.31662479 and -3.31662479.Subproblem 1
q + -6 = 3.31662479 Simplifying q + -6 = 3.31662479 Reorder the terms: -6 + q = 3.31662479 Solving -6 + q = 3.31662479 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = 3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + q = 3.31662479 + 6 q = 3.31662479 + 6 Combine like terms: 3.31662479 + 6 = 9.31662479 q = 9.31662479 Simplifying q = 9.31662479Subproblem 2
q + -6 = -3.31662479 Simplifying q + -6 = -3.31662479 Reorder the terms: -6 + q = -3.31662479 Solving -6 + q = -3.31662479 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = -3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + q = -3.31662479 + 6 q = -3.31662479 + 6 Combine like terms: -3.31662479 + 6 = 2.68337521 q = 2.68337521 Simplifying q = 2.68337521Solution
The solution to the problem is based on the solutions from the subproblems. q = {9.31662479, 2.68337521}Solution
q = {9.31662479, 2.68337521}
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