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Simplifying 0 = 100 + 36q + -4q2 Solving 0 = 100 + 36q + -4q2 Solving for variable 'q'. Combine like terms: 0 + -100 = -100 -100 + -36q + 4q2 = 100 + 36q + -4q2 + -100 + -36q + 4q2 Reorder the terms: -100 + -36q + 4q2 = 100 + -100 + 36q + -36q + -4q2 + 4q2 Combine like terms: 100 + -100 = 0 -100 + -36q + 4q2 = 0 + 36q + -36q + -4q2 + 4q2 -100 + -36q + 4q2 = 36q + -36q + -4q2 + 4q2 Combine like terms: 36q + -36q = 0 -100 + -36q + 4q2 = 0 + -4q2 + 4q2 -100 + -36q + 4q2 = -4q2 + 4q2 Combine like terms: -4q2 + 4q2 = 0 -100 + -36q + 4q2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -9q + q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -9q + q2)' equal to zero and attempt to solve: Simplifying -25 + -9q + q2 = 0 Solving -25 + -9q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -9q + 25 + q2 = 0 + 25 Reorder the terms: -25 + 25 + -9q + q2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -9q + q2 = 0 + 25 -9q + q2 = 0 + 25 Combine like terms: 0 + 25 = 25 -9q + q2 = 25 The q term is -9q. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9q + 20.25 + q2 = 25 + 20.25 Reorder the terms: 20.25 + -9q + q2 = 25 + 20.25 Combine like terms: 25 + 20.25 = 45.25 20.25 + -9q + q2 = 45.25 Factor a perfect square on the left side: (q + -4.5)(q + -4.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (q + -4.5) equal to 6.726812024 and -6.726812024.Subproblem 1
q + -4.5 = 6.726812024 Simplifying q + -4.5 = 6.726812024 Reorder the terms: -4.5 + q = 6.726812024 Solving -4.5 + q = 6.726812024 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + q = 6.726812024 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + q = 6.726812024 + 4.5 q = 6.726812024 + 4.5 Combine like terms: 6.726812024 + 4.5 = 11.226812024 q = 11.226812024 Simplifying q = 11.226812024Subproblem 2
q + -4.5 = -6.726812024 Simplifying q + -4.5 = -6.726812024 Reorder the terms: -4.5 + q = -6.726812024 Solving -4.5 + q = -6.726812024 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + q = -6.726812024 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + q = -6.726812024 + 4.5 q = -6.726812024 + 4.5 Combine like terms: -6.726812024 + 4.5 = -2.226812024 q = -2.226812024 Simplifying q = -2.226812024Solution
The solution to the problem is based on the solutions from the subproblems. q = {11.226812024, -2.226812024}Solution
q = {11.226812024, -2.226812024}
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