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Simplifying 0.35t2 + -50t + 1000 = 0 Reorder the terms: 1000 + -50t + 0.35t2 = 0 Solving 1000 + -50t + 0.35t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. 2857.142857 + -142.8571429t + t2 = 0 Move the constant term to the right: Add '-2857.142857' to each side of the equation. 2857.142857 + -142.8571429t + -2857.142857 + t2 = 0 + -2857.142857 Reorder the terms: 2857.142857 + -2857.142857 + -142.8571429t + t2 = 0 + -2857.142857 Combine like terms: 2857.142857 + -2857.142857 = 0.000000 0.000000 + -142.8571429t + t2 = 0 + -2857.142857 -142.8571429t + t2 = 0 + -2857.142857 Combine like terms: 0 + -2857.142857 = -2857.142857 -142.8571429t + t2 = -2857.142857 The t term is -142.8571429t. Take half its coefficient (-71.42857145). Square it (5102.040819) and add it to both sides. Add '5102.040819' to each side of the equation. -142.8571429t + 5102.040819 + t2 = -2857.142857 + 5102.040819 Reorder the terms: 5102.040819 + -142.8571429t + t2 = -2857.142857 + 5102.040819 Combine like terms: -2857.142857 + 5102.040819 = 2244.897962 5102.040819 + -142.8571429t + t2 = 2244.897962 Factor a perfect square on the left side: (t + -71.42857145)(t + -71.42857145) = 2244.897962 Calculate the square root of the right side: 47.380354178 Break this problem into two subproblems by setting (t + -71.42857145) equal to 47.380354178 and -47.380354178.Subproblem 1
t + -71.42857145 = 47.380354178 Simplifying t + -71.42857145 = 47.380354178 Reorder the terms: -71.42857145 + t = 47.380354178 Solving -71.42857145 + t = 47.380354178 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '71.42857145' to each side of the equation. -71.42857145 + 71.42857145 + t = 47.380354178 + 71.42857145 Combine like terms: -71.42857145 + 71.42857145 = 0.00000000 0.00000000 + t = 47.380354178 + 71.42857145 t = 47.380354178 + 71.42857145 Combine like terms: 47.380354178 + 71.42857145 = 118.808925628 t = 118.808925628 Simplifying t = 118.808925628Subproblem 2
t + -71.42857145 = -47.380354178 Simplifying t + -71.42857145 = -47.380354178 Reorder the terms: -71.42857145 + t = -47.380354178 Solving -71.42857145 + t = -47.380354178 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '71.42857145' to each side of the equation. -71.42857145 + 71.42857145 + t = -47.380354178 + 71.42857145 Combine like terms: -71.42857145 + 71.42857145 = 0.00000000 0.00000000 + t = -47.380354178 + 71.42857145 t = -47.380354178 + 71.42857145 Combine like terms: -47.380354178 + 71.42857145 = 24.048217272 t = 24.048217272 Simplifying t = 24.048217272Solution
The solution to the problem is based on the solutions from the subproblems. t = {118.808925628, 24.048217272}
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