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Simplifying 6q(7q + -2) = 58 Reorder the terms: 6q(-2 + 7q) = 58 (-2 * 6q + 7q * 6q) = 58 (-12q + 42q2) = 58 Solving -12q + 42q2 = 58 Solving for variable 'q'. Reorder the terms: -58 + -12q + 42q2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -12q + 42q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -6q + 21q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -6q + 21q2)' equal to zero and attempt to solve: Simplifying -29 + -6q + 21q2 = 0 Solving -29 + -6q + 21q2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.380952381 + -0.2857142857q + q2 = 0 Move the constant term to the right: Add '1.380952381' to each side of the equation. -1.380952381 + -0.2857142857q + 1.380952381 + q2 = 0 + 1.380952381 Reorder the terms: -1.380952381 + 1.380952381 + -0.2857142857q + q2 = 0 + 1.380952381 Combine like terms: -1.380952381 + 1.380952381 = 0.000000000 0.000000000 + -0.2857142857q + q2 = 0 + 1.380952381 -0.2857142857q + q2 = 0 + 1.380952381 Combine like terms: 0 + 1.380952381 = 1.380952381 -0.2857142857q + q2 = 1.380952381 The q term is -0.2857142857q. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857q + 0.02040816328 + q2 = 1.380952381 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857q + q2 = 1.380952381 + 0.02040816328 Combine like terms: 1.380952381 + 0.02040816328 = 1.40136054428 0.02040816328 + -0.2857142857q + q2 = 1.40136054428 Factor a perfect square on the left side: (q + -0.1428571429)(q + -0.1428571429) = 1.40136054428 Calculate the square root of the right side: 1.183790752 Break this problem into two subproblems by setting (q + -0.1428571429) equal to 1.183790752 and -1.183790752.Subproblem 1
q + -0.1428571429 = 1.183790752 Simplifying q + -0.1428571429 = 1.183790752 Reorder the terms: -0.1428571429 + q = 1.183790752 Solving -0.1428571429 + q = 1.183790752 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + q = 1.183790752 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + q = 1.183790752 + 0.1428571429 q = 1.183790752 + 0.1428571429 Combine like terms: 1.183790752 + 0.1428571429 = 1.3266478949 q = 1.3266478949 Simplifying q = 1.3266478949Subproblem 2
q + -0.1428571429 = -1.183790752 Simplifying q + -0.1428571429 = -1.183790752 Reorder the terms: -0.1428571429 + q = -1.183790752 Solving -0.1428571429 + q = -1.183790752 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + q = -1.183790752 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + q = -1.183790752 + 0.1428571429 q = -1.183790752 + 0.1428571429 Combine like terms: -1.183790752 + 0.1428571429 = -1.0409336091 q = -1.0409336091 Simplifying q = -1.0409336091Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.3266478949, -1.0409336091}Solution
q = {1.3266478949, -1.0409336091}
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