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Simplifying q2 + -48q + 420 = 0 Reorder the terms: 420 + -48q + q2 = 0 Solving 420 + -48q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-420' to each side of the equation. 420 + -48q + -420 + q2 = 0 + -420 Reorder the terms: 420 + -420 + -48q + q2 = 0 + -420 Combine like terms: 420 + -420 = 0 0 + -48q + q2 = 0 + -420 -48q + q2 = 0 + -420 Combine like terms: 0 + -420 = -420 -48q + q2 = -420 The q term is -48q. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48q + 576 + q2 = -420 + 576 Reorder the terms: 576 + -48q + q2 = -420 + 576 Combine like terms: -420 + 576 = 156 576 + -48q + q2 = 156 Factor a perfect square on the left side: (q + -24)(q + -24) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (q + -24) equal to 12.489995997 and -12.489995997.Subproblem 1
q + -24 = 12.489995997 Simplifying q + -24 = 12.489995997 Reorder the terms: -24 + q = 12.489995997 Solving -24 + q = 12.489995997 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + q = 12.489995997 + 24 Combine like terms: -24 + 24 = 0 0 + q = 12.489995997 + 24 q = 12.489995997 + 24 Combine like terms: 12.489995997 + 24 = 36.489995997 q = 36.489995997 Simplifying q = 36.489995997Subproblem 2
q + -24 = -12.489995997 Simplifying q + -24 = -12.489995997 Reorder the terms: -24 + q = -12.489995997 Solving -24 + q = -12.489995997 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + q = -12.489995997 + 24 Combine like terms: -24 + 24 = 0 0 + q = -12.489995997 + 24 q = -12.489995997 + 24 Combine like terms: -12.489995997 + 24 = 11.510004003 q = 11.510004003 Simplifying q = 11.510004003Solution
The solution to the problem is based on the solutions from the subproblems. q = {36.489995997, 11.510004003}
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