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Simplifying 6q2 + -1q + -800 = 0 Reorder the terms: -800 + -1q + 6q2 = 0 Solving -800 + -1q + 6q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -133.3333333 + -0.1666666667q + q2 = 0 Move the constant term to the right: Add '133.3333333' to each side of the equation. -133.3333333 + -0.1666666667q + 133.3333333 + q2 = 0 + 133.3333333 Reorder the terms: -133.3333333 + 133.3333333 + -0.1666666667q + q2 = 0 + 133.3333333 Combine like terms: -133.3333333 + 133.3333333 = 0.0000000 0.0000000 + -0.1666666667q + q2 = 0 + 133.3333333 -0.1666666667q + q2 = 0 + 133.3333333 Combine like terms: 0 + 133.3333333 = 133.3333333 -0.1666666667q + q2 = 133.3333333 The q term is -0.1666666667q. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667q + 0.006944444447 + q2 = 133.3333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667q + q2 = 133.3333333 + 0.006944444447 Combine like terms: 133.3333333 + 0.006944444447 = 133.340277744447 0.006944444447 + -0.1666666667q + q2 = 133.340277744447 Factor a perfect square on the left side: (q + -0.08333333335)(q + -0.08333333335) = 133.340277744447 Calculate the square root of the right side: 11.547306082 Break this problem into two subproblems by setting (q + -0.08333333335) equal to 11.547306082 and -11.547306082.Subproblem 1
q + -0.08333333335 = 11.547306082 Simplifying q + -0.08333333335 = 11.547306082 Reorder the terms: -0.08333333335 + q = 11.547306082 Solving -0.08333333335 + q = 11.547306082 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + q = 11.547306082 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + q = 11.547306082 + 0.08333333335 q = 11.547306082 + 0.08333333335 Combine like terms: 11.547306082 + 0.08333333335 = 11.63063941535 q = 11.63063941535 Simplifying q = 11.63063941535Subproblem 2
q + -0.08333333335 = -11.547306082 Simplifying q + -0.08333333335 = -11.547306082 Reorder the terms: -0.08333333335 + q = -11.547306082 Solving -0.08333333335 + q = -11.547306082 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + q = -11.547306082 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + q = -11.547306082 + 0.08333333335 q = -11.547306082 + 0.08333333335 Combine like terms: -11.547306082 + 0.08333333335 = -11.46397274865 q = -11.46397274865 Simplifying q = -11.46397274865Solution
The solution to the problem is based on the solutions from the subproblems. q = {11.63063941535, -11.46397274865}
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