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Simplifying 7q(3q + 14) = 18 Reorder the terms: 7q(14 + 3q) = 18 (14 * 7q + 3q * 7q) = 18 (98q + 21q2) = 18 Solving 98q + 21q2 = 18 Solving for variable 'q'. Reorder the terms: -18 + 98q + 21q2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 98q + 21q2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.8571428571 + 4.666666667q + q2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 4.666666667q + 0.8571428571 + q2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 4.666666667q + q2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 4.666666667q + q2 = 0 + 0.8571428571 4.666666667q + q2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 4.666666667q + q2 = 0.8571428571 The q term is 4.666666667q. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667q + 5.444444448 + q2 = 0.8571428571 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667q + q2 = 0.8571428571 + 5.444444448 Combine like terms: 0.8571428571 + 5.444444448 = 6.3015873051 5.444444448 + 4.666666667q + q2 = 6.3015873051 Factor a perfect square on the left side: (q + 2.333333334)(q + 2.333333334) = 6.3015873051 Calculate the square root of the right side: 2.510296258 Break this problem into two subproblems by setting (q + 2.333333334) equal to 2.510296258 and -2.510296258.Subproblem 1
q + 2.333333334 = 2.510296258 Simplifying q + 2.333333334 = 2.510296258 Reorder the terms: 2.333333334 + q = 2.510296258 Solving 2.333333334 + q = 2.510296258 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + q = 2.510296258 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + q = 2.510296258 + -2.333333334 q = 2.510296258 + -2.333333334 Combine like terms: 2.510296258 + -2.333333334 = 0.176962924 q = 0.176962924 Simplifying q = 0.176962924Subproblem 2
q + 2.333333334 = -2.510296258 Simplifying q + 2.333333334 = -2.510296258 Reorder the terms: 2.333333334 + q = -2.510296258 Solving 2.333333334 + q = -2.510296258 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + q = -2.510296258 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + q = -2.510296258 + -2.333333334 q = -2.510296258 + -2.333333334 Combine like terms: -2.510296258 + -2.333333334 = -4.843629592 q = -4.843629592 Simplifying q = -4.843629592Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.176962924, -4.843629592}
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