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Simplifying -3t2 + 500t + 200 = 0 Reorder the terms: 200 + 500t + -3t2 = 0 Solving 200 + 500t + -3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -66.66666667 + -166.6666667t + t2 = 0 Move the constant term to the right: Add '66.66666667' to each side of the equation. -66.66666667 + -166.6666667t + 66.66666667 + t2 = 0 + 66.66666667 Reorder the terms: -66.66666667 + 66.66666667 + -166.6666667t + t2 = 0 + 66.66666667 Combine like terms: -66.66666667 + 66.66666667 = 0.00000000 0.00000000 + -166.6666667t + t2 = 0 + 66.66666667 -166.6666667t + t2 = 0 + 66.66666667 Combine like terms: 0 + 66.66666667 = 66.66666667 -166.6666667t + t2 = 66.66666667 The t term is -166.6666667t. 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. -166.6666667t + 6944.444447 + t2 = 66.66666667 + 6944.444447 Reorder the terms: 6944.444447 + -166.6666667t + t2 = 66.66666667 + 6944.444447 Combine like terms: 66.66666667 + 6944.444447 = 7011.11111367 6944.444447 + -166.6666667t + t2 = 7011.11111367 Factor a perfect square on the left side: (t + -83.33333335)(t + -83.33333335) = 7011.11111367 Calculate the square root of the right side: 83.732377929 Break this problem into two subproblems by setting (t + -83.33333335) equal to 83.732377929 and -83.732377929.Subproblem 1
t + -83.33333335 = 83.732377929 Simplifying t + -83.33333335 = 83.732377929 Reorder the terms: -83.33333335 + t = 83.732377929 Solving -83.33333335 + t = 83.732377929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '83.33333335' to each side of the equation. -83.33333335 + 83.33333335 + t = 83.732377929 + 83.33333335 Combine like terms: -83.33333335 + 83.33333335 = 0.00000000 0.00000000 + t = 83.732377929 + 83.33333335 t = 83.732377929 + 83.33333335 Combine like terms: 83.732377929 + 83.33333335 = 167.065711279 t = 167.065711279 Simplifying t = 167.065711279Subproblem 2
t + -83.33333335 = -83.732377929 Simplifying t + -83.33333335 = -83.732377929 Reorder the terms: -83.33333335 + t = -83.732377929 Solving -83.33333335 + t = -83.732377929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '83.33333335' to each side of the equation. -83.33333335 + 83.33333335 + t = -83.732377929 + 83.33333335 Combine like terms: -83.33333335 + 83.33333335 = 0.00000000 0.00000000 + t = -83.732377929 + 83.33333335 t = -83.732377929 + 83.33333335 Combine like terms: -83.732377929 + 83.33333335 = -0.399044579 t = -0.399044579 Simplifying t = -0.399044579Solution
The solution to the problem is based on the solutions from the subproblems. t = {167.065711279, -0.399044579}
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