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Simplifying 200 = 3Q2 + -24Q + 95 Reorder the terms: 200 = 95 + -24Q + 3Q2 Solving 200 = 95 + -24Q + 3Q2 Solving for variable 'Q'. Combine like terms: 200 + -95 = 105 105 + 24Q + -3Q2 = 95 + -24Q + 3Q2 + -95 + 24Q + -3Q2 Reorder the terms: 105 + 24Q + -3Q2 = 95 + -95 + -24Q + 24Q + 3Q2 + -3Q2 Combine like terms: 95 + -95 = 0 105 + 24Q + -3Q2 = 0 + -24Q + 24Q + 3Q2 + -3Q2 105 + 24Q + -3Q2 = -24Q + 24Q + 3Q2 + -3Q2 Combine like terms: -24Q + 24Q = 0 105 + 24Q + -3Q2 = 0 + 3Q2 + -3Q2 105 + 24Q + -3Q2 = 3Q2 + -3Q2 Combine like terms: 3Q2 + -3Q2 = 0 105 + 24Q + -3Q2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(35 + 8Q + -1Q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(35 + 8Q + -1Q2)' equal to zero and attempt to solve: Simplifying 35 + 8Q + -1Q2 = 0 Solving 35 + 8Q + -1Q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + -8Q + Q2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -8Q + 35 + Q2 = 0 + 35 Reorder the terms: -35 + 35 + -8Q + Q2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -8Q + Q2 = 0 + 35 -8Q + Q2 = 0 + 35 Combine like terms: 0 + 35 = 35 -8Q + Q2 = 35 The Q term is -8Q. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8Q + 16 + Q2 = 35 + 16 Reorder the terms: 16 + -8Q + Q2 = 35 + 16 Combine like terms: 35 + 16 = 51 16 + -8Q + Q2 = 51 Factor a perfect square on the left side: (Q + -4)(Q + -4) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (Q + -4) equal to 7.141428429 and -7.141428429.Subproblem 1
Q + -4 = 7.141428429 Simplifying Q + -4 = 7.141428429 Reorder the terms: -4 + Q = 7.141428429 Solving -4 + Q = 7.141428429 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + Q = 7.141428429 + 4 Combine like terms: -4 + 4 = 0 0 + Q = 7.141428429 + 4 Q = 7.141428429 + 4 Combine like terms: 7.141428429 + 4 = 11.141428429 Q = 11.141428429 Simplifying Q = 11.141428429Subproblem 2
Q + -4 = -7.141428429 Simplifying Q + -4 = -7.141428429 Reorder the terms: -4 + Q = -7.141428429 Solving -4 + Q = -7.141428429 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + Q = -7.141428429 + 4 Combine like terms: -4 + 4 = 0 0 + Q = -7.141428429 + 4 Q = -7.141428429 + 4 Combine like terms: -7.141428429 + 4 = -3.141428429 Q = -3.141428429 Simplifying Q = -3.141428429Solution
The solution to the problem is based on the solutions from the subproblems. Q = {11.141428429, -3.141428429}Solution
Q = {11.141428429, -3.141428429}
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