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Simplifying 150 + -10q + 2q2 = 200 + 40q Solving 150 + -10q + 2q2 = 200 + 40q Solving for variable 'q'. Reorder the terms: 150 + -200 + -10q + -40q + 2q2 = 200 + 40q + -200 + -40q Combine like terms: 150 + -200 = -50 -50 + -10q + -40q + 2q2 = 200 + 40q + -200 + -40q Combine like terms: -10q + -40q = -50q -50 + -50q + 2q2 = 200 + 40q + -200 + -40q Reorder the terms: -50 + -50q + 2q2 = 200 + -200 + 40q + -40q Combine like terms: 200 + -200 = 0 -50 + -50q + 2q2 = 0 + 40q + -40q -50 + -50q + 2q2 = 40q + -40q Combine like terms: 40q + -40q = 0 -50 + -50q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -25q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -25q + q2)' equal to zero and attempt to solve: Simplifying -25 + -25q + q2 = 0 Solving -25 + -25q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -25q + 25 + q2 = 0 + 25 Reorder the terms: -25 + 25 + -25q + q2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -25q + q2 = 0 + 25 -25q + q2 = 0 + 25 Combine like terms: 0 + 25 = 25 -25q + q2 = 25 The q term is -25q. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25q + 156.25 + q2 = 25 + 156.25 Reorder the terms: 156.25 + -25q + q2 = 25 + 156.25 Combine like terms: 25 + 156.25 = 181.25 156.25 + -25q + q2 = 181.25 Factor a perfect square on the left side: (q + -12.5)(q + -12.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (q + -12.5) equal to 13.462912018 and -13.462912018.Subproblem 1
q + -12.5 = 13.462912018 Simplifying q + -12.5 = 13.462912018 Reorder the terms: -12.5 + q = 13.462912018 Solving -12.5 + q = 13.462912018 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + q = 13.462912018 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + q = 13.462912018 + 12.5 q = 13.462912018 + 12.5 Combine like terms: 13.462912018 + 12.5 = 25.962912018 q = 25.962912018 Simplifying q = 25.962912018Subproblem 2
q + -12.5 = -13.462912018 Simplifying q + -12.5 = -13.462912018 Reorder the terms: -12.5 + q = -13.462912018 Solving -12.5 + q = -13.462912018 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + q = -13.462912018 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + q = -13.462912018 + 12.5 q = -13.462912018 + 12.5 Combine like terms: -13.462912018 + 12.5 = -0.962912018 q = -0.962912018 Simplifying q = -0.962912018Solution
The solution to the problem is based on the solutions from the subproblems. q = {25.962912018, -0.962912018}Solution
q = {25.962912018, -0.962912018}
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