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Simplifying 0 = -1.75t2 + 30t + 6 Reorder the terms: 0 = 6 + 30t + -1.75t2 Solving 0 = 6 + 30t + -1.75t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -30t + 1.75t2 = 6 + 30t + -1.75t2 + -6 + -30t + 1.75t2 Reorder the terms: -6 + -30t + 1.75t2 = 6 + -6 + 30t + -30t + -1.75t2 + 1.75t2 Combine like terms: 6 + -6 = 0 -6 + -30t + 1.75t2 = 0 + 30t + -30t + -1.75t2 + 1.75t2 -6 + -30t + 1.75t2 = 30t + -30t + -1.75t2 + 1.75t2 Combine like terms: 30t + -30t = 0 -6 + -30t + 1.75t2 = 0 + -1.75t2 + 1.75t2 -6 + -30t + 1.75t2 = -1.75t2 + 1.75t2 Combine like terms: -1.75t2 + 1.75t2 = 0.00 -6 + -30t + 1.75t2 = 0.00 Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -3.428571429 + -17.14285714t + t2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -17.14285714t + 3.428571429 + t2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -17.14285714t + t2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -17.14285714t + t2 = 0 + 3.428571429 -17.14285714t + t2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -17.14285714t + t2 = 3.428571429 The t term is -17.14285714t. Take half its coefficient (-8.57142857). Square it (73.46938773) and add it to both sides. Add '73.46938773' to each side of the equation. -17.14285714t + 73.46938773 + t2 = 3.428571429 + 73.46938773 Reorder the terms: 73.46938773 + -17.14285714t + t2 = 3.428571429 + 73.46938773 Combine like terms: 3.428571429 + 73.46938773 = 76.897959159 73.46938773 + -17.14285714t + t2 = 76.897959159 Factor a perfect square on the left side: (t + -8.57142857)(t + -8.57142857) = 76.897959159 Calculate the square root of the right side: 8.769148143 Break this problem into two subproblems by setting (t + -8.57142857) equal to 8.769148143 and -8.769148143.Subproblem 1
t + -8.57142857 = 8.769148143 Simplifying t + -8.57142857 = 8.769148143 Reorder the terms: -8.57142857 + t = 8.769148143 Solving -8.57142857 + t = 8.769148143 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.57142857' to each side of the equation. -8.57142857 + 8.57142857 + t = 8.769148143 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + t = 8.769148143 + 8.57142857 t = 8.769148143 + 8.57142857 Combine like terms: 8.769148143 + 8.57142857 = 17.340576713 t = 17.340576713 Simplifying t = 17.340576713Subproblem 2
t + -8.57142857 = -8.769148143 Simplifying t + -8.57142857 = -8.769148143 Reorder the terms: -8.57142857 + t = -8.769148143 Solving -8.57142857 + t = -8.769148143 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.57142857' to each side of the equation. -8.57142857 + 8.57142857 + t = -8.769148143 + 8.57142857 Combine like terms: -8.57142857 + 8.57142857 = 0.00000000 0.00000000 + t = -8.769148143 + 8.57142857 t = -8.769148143 + 8.57142857 Combine like terms: -8.769148143 + 8.57142857 = -0.197719573 t = -0.197719573 Simplifying t = -0.197719573Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.340576713, -0.197719573}
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