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Simplifying -3q2 + -24q + 300 = 0 Reorder the terms: 300 + -24q + -3q2 = 0 Solving 300 + -24q + -3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(100 + -8q + -1q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(100 + -8q + -1q2)' equal to zero and attempt to solve: Simplifying 100 + -8q + -1q2 = 0 Solving 100 + -8q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 8q + q2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 8q + 100 + q2 = 0 + 100 Reorder the terms: -100 + 100 + 8q + q2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 8q + q2 = 0 + 100 8q + q2 = 0 + 100 Combine like terms: 0 + 100 = 100 8q + q2 = 100 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 = 100 + 16 Reorder the terms: 16 + 8q + q2 = 100 + 16 Combine like terms: 100 + 16 = 116 16 + 8q + q2 = 116 Factor a perfect square on the left side: (q + 4)(q + 4) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (q + 4) equal to 10.770329614 and -10.770329614.Subproblem 1
q + 4 = 10.770329614 Simplifying q + 4 = 10.770329614 Reorder the terms: 4 + q = 10.770329614 Solving 4 + q = 10.770329614 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 = 10.770329614 + -4 Combine like terms: 4 + -4 = 0 0 + q = 10.770329614 + -4 q = 10.770329614 + -4 Combine like terms: 10.770329614 + -4 = 6.770329614 q = 6.770329614 Simplifying q = 6.770329614Subproblem 2
q + 4 = -10.770329614 Simplifying q + 4 = -10.770329614 Reorder the terms: 4 + q = -10.770329614 Solving 4 + q = -10.770329614 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 = -10.770329614 + -4 Combine like terms: 4 + -4 = 0 0 + q = -10.770329614 + -4 q = -10.770329614 + -4 Combine like terms: -10.770329614 + -4 = -14.770329614 q = -14.770329614 Simplifying q = -14.770329614Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.770329614, -14.770329614}Solution
q = {6.770329614, -14.770329614}
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