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Simplifying q2 + -30q + 19 = -36 Reorder the terms: 19 + -30q + q2 = -36 Solving 19 + -30q + q2 = -36 Solving for variable 'q'. Reorder the terms: 19 + 36 + -30q + q2 = -36 + 36 Combine like terms: 19 + 36 = 55 55 + -30q + q2 = -36 + 36 Combine like terms: -36 + 36 = 0 55 + -30q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -30q + -55 + q2 = 0 + -55 Reorder the terms: 55 + -55 + -30q + q2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -30q + q2 = 0 + -55 -30q + q2 = 0 + -55 Combine like terms: 0 + -55 = -55 -30q + q2 = -55 The q term is -30q. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30q + 225 + q2 = -55 + 225 Reorder the terms: 225 + -30q + q2 = -55 + 225 Combine like terms: -55 + 225 = 170 225 + -30q + q2 = 170 Factor a perfect square on the left side: (q + -15)(q + -15) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (q + -15) equal to 13.03840481 and -13.03840481.Subproblem 1
q + -15 = 13.03840481 Simplifying q + -15 = 13.03840481 Reorder the terms: -15 + q = 13.03840481 Solving -15 + q = 13.03840481 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + q = 13.03840481 + 15 Combine like terms: -15 + 15 = 0 0 + q = 13.03840481 + 15 q = 13.03840481 + 15 Combine like terms: 13.03840481 + 15 = 28.03840481 q = 28.03840481 Simplifying q = 28.03840481Subproblem 2
q + -15 = -13.03840481 Simplifying q + -15 = -13.03840481 Reorder the terms: -15 + q = -13.03840481 Solving -15 + q = -13.03840481 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + q = -13.03840481 + 15 Combine like terms: -15 + 15 = 0 0 + q = -13.03840481 + 15 q = -13.03840481 + 15 Combine like terms: -13.03840481 + 15 = 1.96159519 q = 1.96159519 Simplifying q = 1.96159519Solution
The solution to the problem is based on the solutions from the subproblems. q = {28.03840481, 1.96159519}
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