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Simplifying 12 + q2 + -30q = 0 Reorder the terms: 12 + -30q + q2 = 0 Solving 12 + -30q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -30q + -12 + q2 = 0 + -12 Reorder the terms: 12 + -12 + -30q + q2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -30q + q2 = 0 + -12 -30q + q2 = 0 + -12 Combine like terms: 0 + -12 = -12 -30q + q2 = -12 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 = -12 + 225 Reorder the terms: 225 + -30q + q2 = -12 + 225 Combine like terms: -12 + 225 = 213 225 + -30q + q2 = 213 Factor a perfect square on the left side: (q + -15)(q + -15) = 213 Calculate the square root of the right side: 14.594519519 Break this problem into two subproblems by setting (q + -15) equal to 14.594519519 and -14.594519519.Subproblem 1
q + -15 = 14.594519519 Simplifying q + -15 = 14.594519519 Reorder the terms: -15 + q = 14.594519519 Solving -15 + q = 14.594519519 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 = 14.594519519 + 15 Combine like terms: -15 + 15 = 0 0 + q = 14.594519519 + 15 q = 14.594519519 + 15 Combine like terms: 14.594519519 + 15 = 29.594519519 q = 29.594519519 Simplifying q = 29.594519519Subproblem 2
q + -15 = -14.594519519 Simplifying q + -15 = -14.594519519 Reorder the terms: -15 + q = -14.594519519 Solving -15 + q = -14.594519519 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 = -14.594519519 + 15 Combine like terms: -15 + 15 = 0 0 + q = -14.594519519 + 15 q = -14.594519519 + 15 Combine like terms: -14.594519519 + 15 = 0.405480481 q = 0.405480481 Simplifying q = 0.405480481Solution
The solution to the problem is based on the solutions from the subproblems. q = {29.594519519, 0.405480481}
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