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Simplifying 48Q + -1(12 + 12Q + 3Q2) = 0 48Q + (12 * -1 + 12Q * -1 + 3Q2 * -1) = 0 48Q + (-12 + -12Q + -3Q2) = 0 Reorder the terms: -12 + 48Q + -12Q + -3Q2 = 0 Combine like terms: 48Q + -12Q = 36Q -12 + 36Q + -3Q2 = 0 Solving -12 + 36Q + -3Q2 = 0 Solving for variable 'Q'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 12Q + -1Q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 12Q + -1Q2)' equal to zero and attempt to solve: Simplifying -4 + 12Q + -1Q2 = 0 Solving -4 + 12Q + -1Q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -12Q + Q2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -12Q + -4 + Q2 = 0 + -4 Reorder the terms: 4 + -4 + -12Q + Q2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -12Q + Q2 = 0 + -4 -12Q + Q2 = 0 + -4 Combine like terms: 0 + -4 = -4 -12Q + Q2 = -4 The Q term is -12Q. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12Q + 36 + Q2 = -4 + 36 Reorder the terms: 36 + -12Q + Q2 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + -12Q + Q2 = 32 Factor a perfect square on the left side: (Q + -6)(Q + -6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (Q + -6) equal to 5.656854249 and -5.656854249.Subproblem 1
Q + -6 = 5.656854249 Simplifying Q + -6 = 5.656854249 Reorder the terms: -6 + Q = 5.656854249 Solving -6 + Q = 5.656854249 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + Q = 5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + Q = 5.656854249 + 6 Q = 5.656854249 + 6 Combine like terms: 5.656854249 + 6 = 11.656854249 Q = 11.656854249 Simplifying Q = 11.656854249Subproblem 2
Q + -6 = -5.656854249 Simplifying Q + -6 = -5.656854249 Reorder the terms: -6 + Q = -5.656854249 Solving -6 + Q = -5.656854249 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + Q = -5.656854249 + 6 Combine like terms: -6 + 6 = 0 0 + Q = -5.656854249 + 6 Q = -5.656854249 + 6 Combine like terms: -5.656854249 + 6 = 0.343145751 Q = 0.343145751 Simplifying Q = 0.343145751Solution
The solution to the problem is based on the solutions from the subproblems. Q = {11.656854249, 0.343145751}Solution
Q = {11.656854249, 0.343145751}
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