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Simplifying 2q * q + -118.5q + 328.5 = 0 Multiply q * q 2q2 + -118.5q + 328.5 = 0 Reorder the terms: 328.5 + -118.5q + 2q2 = 0 Solving 328.5 + -118.5q + 2q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 164.25 + -59.25q + q2 = 0 Move the constant term to the right: Add '-164.25' to each side of the equation. 164.25 + -59.25q + -164.25 + q2 = 0 + -164.25 Reorder the terms: 164.25 + -164.25 + -59.25q + q2 = 0 + -164.25 Combine like terms: 164.25 + -164.25 = 0.00 0.00 + -59.25q + q2 = 0 + -164.25 -59.25q + q2 = 0 + -164.25 Combine like terms: 0 + -164.25 = -164.25 -59.25q + q2 = -164.25 The q term is -59.25q. Take half its coefficient (-29.625). Square it (877.640625) and add it to both sides. Add '877.640625' to each side of the equation. -59.25q + 877.640625 + q2 = -164.25 + 877.640625 Reorder the terms: 877.640625 + -59.25q + q2 = -164.25 + 877.640625 Combine like terms: -164.25 + 877.640625 = 713.390625 877.640625 + -59.25q + q2 = 713.390625 Factor a perfect square on the left side: (q + -29.625)(q + -29.625) = 713.390625 Calculate the square root of the right side: 26.709373355 Break this problem into two subproblems by setting (q + -29.625) equal to 26.709373355 and -26.709373355.Subproblem 1
q + -29.625 = 26.709373355 Simplifying q + -29.625 = 26.709373355 Reorder the terms: -29.625 + q = 26.709373355 Solving -29.625 + q = 26.709373355 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '29.625' to each side of the equation. -29.625 + 29.625 + q = 26.709373355 + 29.625 Combine like terms: -29.625 + 29.625 = 0.000 0.000 + q = 26.709373355 + 29.625 q = 26.709373355 + 29.625 Combine like terms: 26.709373355 + 29.625 = 56.334373355 q = 56.334373355 Simplifying q = 56.334373355Subproblem 2
q + -29.625 = -26.709373355 Simplifying q + -29.625 = -26.709373355 Reorder the terms: -29.625 + q = -26.709373355 Solving -29.625 + q = -26.709373355 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '29.625' to each side of the equation. -29.625 + 29.625 + q = -26.709373355 + 29.625 Combine like terms: -29.625 + 29.625 = 0.000 0.000 + q = -26.709373355 + 29.625 q = -26.709373355 + 29.625 Combine like terms: -26.709373355 + 29.625 = 2.915626645 q = 2.915626645 Simplifying q = 2.915626645Solution
The solution to the problem is based on the solutions from the subproblems. q = {56.334373355, 2.915626645}
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