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Simplifying 100 + 36Q + -4Q2 = 0 Solving 100 + 36Q + -4Q2 = 0 Solving for variable 'Q'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 9Q + -1Q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 9Q + -1Q2)' equal to zero and attempt to solve: Simplifying 25 + 9Q + -1Q2 = 0 Solving 25 + 9Q + -1Q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -9Q + Q2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -9Q + 25 + Q2 = 0 + 25 Reorder the terms: -25 + 25 + -9Q + Q2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -9Q + Q2 = 0 + 25 -9Q + Q2 = 0 + 25 Combine like terms: 0 + 25 = 25 -9Q + Q2 = 25 The Q term is -9Q. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9Q + 20.25 + Q2 = 25 + 20.25 Reorder the terms: 20.25 + -9Q + Q2 = 25 + 20.25 Combine like terms: 25 + 20.25 = 45.25 20.25 + -9Q + Q2 = 45.25 Factor a perfect square on the left side: (Q + -4.5)(Q + -4.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (Q + -4.5) equal to 6.726812024 and -6.726812024.Subproblem 1
Q + -4.5 = 6.726812024 Simplifying Q + -4.5 = 6.726812024 Reorder the terms: -4.5 + Q = 6.726812024 Solving -4.5 + Q = 6.726812024 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + Q = 6.726812024 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + Q = 6.726812024 + 4.5 Q = 6.726812024 + 4.5 Combine like terms: 6.726812024 + 4.5 = 11.226812024 Q = 11.226812024 Simplifying Q = 11.226812024Subproblem 2
Q + -4.5 = -6.726812024 Simplifying Q + -4.5 = -6.726812024 Reorder the terms: -4.5 + Q = -6.726812024 Solving -4.5 + Q = -6.726812024 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + Q = -6.726812024 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + Q = -6.726812024 + 4.5 Q = -6.726812024 + 4.5 Combine like terms: -6.726812024 + 4.5 = -2.226812024 Q = -2.226812024 Simplifying Q = -2.226812024Solution
The solution to the problem is based on the solutions from the subproblems. Q = {11.226812024, -2.226812024}Solution
Q = {11.226812024, -2.226812024}
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