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Simplifying 20Q + -2Q2 = 4 + 2Q2 Solving 20Q + -2Q2 = 4 + 2Q2 Solving for variable 'Q'. Reorder the terms: -4 + 20Q + -2Q2 + -2Q2 = 4 + 2Q2 + -4 + -2Q2 Combine like terms: -2Q2 + -2Q2 = -4Q2 -4 + 20Q + -4Q2 = 4 + 2Q2 + -4 + -2Q2 Reorder the terms: -4 + 20Q + -4Q2 = 4 + -4 + 2Q2 + -2Q2 Combine like terms: 4 + -4 = 0 -4 + 20Q + -4Q2 = 0 + 2Q2 + -2Q2 -4 + 20Q + -4Q2 = 2Q2 + -2Q2 Combine like terms: 2Q2 + -2Q2 = 0 -4 + 20Q + -4Q2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 5Q + -1Q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + 5Q + -1Q2)' equal to zero and attempt to solve: Simplifying -1 + 5Q + -1Q2 = 0 Solving -1 + 5Q + -1Q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -5Q + Q2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5Q + -1 + Q2 = 0 + -1 Reorder the terms: 1 + -1 + -5Q + Q2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5Q + Q2 = 0 + -1 -5Q + Q2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5Q + Q2 = -1 The Q term is -5Q. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5Q + 6.25 + Q2 = -1 + 6.25 Reorder the terms: 6.25 + -5Q + Q2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5Q + Q2 = 5.25 Factor a perfect square on the left side: (Q + -2.5)(Q + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (Q + -2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
Q + -2.5 = 2.291287847 Simplifying Q + -2.5 = 2.291287847 Reorder the terms: -2.5 + Q = 2.291287847 Solving -2.5 + Q = 2.291287847 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + Q = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + Q = 2.291287847 + 2.5 Q = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 Q = 4.791287847 Simplifying Q = 4.791287847Subproblem 2
Q + -2.5 = -2.291287847 Simplifying Q + -2.5 = -2.291287847 Reorder the terms: -2.5 + Q = -2.291287847 Solving -2.5 + Q = -2.291287847 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + Q = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + Q = -2.291287847 + 2.5 Q = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 Q = 0.208712153 Simplifying Q = 0.208712153Solution
The solution to the problem is based on the solutions from the subproblems. Q = {4.791287847, 0.208712153}Solution
Q = {4.791287847, 0.208712153}
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