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Simplifying -3q2 + 500q + -13 = 0 Reorder the terms: -13 + 500q + -3q2 = 0 Solving -13 + 500q + -3q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4.333333333 + -166.6666667q + q2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -166.6666667q + -4.333333333 + q2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -166.6666667q + q2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -166.6666667q + q2 = 0 + -4.333333333 -166.6666667q + q2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -166.6666667q + q2 = -4.333333333 The q term is -166.6666667q. Take half its coefficient (-83.33333335). Square it (6944.444447) and add it to both sides. Add '6944.444447' to each side of the equation. -166.6666667q + 6944.444447 + q2 = -4.333333333 + 6944.444447 Reorder the terms: 6944.444447 + -166.6666667q + q2 = -4.333333333 + 6944.444447 Combine like terms: -4.333333333 + 6944.444447 = 6940.111113667 6944.444447 + -166.6666667q + q2 = 6940.111113667 Factor a perfect square on the left side: (q + -83.33333335)(q + -83.33333335) = 6940.111113667 Calculate the square root of the right side: 83.307329291 Break this problem into two subproblems by setting (q + -83.33333335) equal to 83.307329291 and -83.307329291.Subproblem 1
q + -83.33333335 = 83.307329291 Simplifying q + -83.33333335 = 83.307329291 Reorder the terms: -83.33333335 + q = 83.307329291 Solving -83.33333335 + q = 83.307329291 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '83.33333335' to each side of the equation. -83.33333335 + 83.33333335 + q = 83.307329291 + 83.33333335 Combine like terms: -83.33333335 + 83.33333335 = 0.00000000 0.00000000 + q = 83.307329291 + 83.33333335 q = 83.307329291 + 83.33333335 Combine like terms: 83.307329291 + 83.33333335 = 166.640662641 q = 166.640662641 Simplifying q = 166.640662641Subproblem 2
q + -83.33333335 = -83.307329291 Simplifying q + -83.33333335 = -83.307329291 Reorder the terms: -83.33333335 + q = -83.307329291 Solving -83.33333335 + q = -83.307329291 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '83.33333335' to each side of the equation. -83.33333335 + 83.33333335 + q = -83.307329291 + 83.33333335 Combine like terms: -83.33333335 + 83.33333335 = 0.00000000 0.00000000 + q = -83.307329291 + 83.33333335 q = -83.307329291 + 83.33333335 Combine like terms: -83.307329291 + 83.33333335 = 0.026004059 q = 0.026004059 Simplifying q = 0.026004059Solution
The solution to the problem is based on the solutions from the subproblems. q = {166.640662641, 0.026004059}
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