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Simplifying 35 = -3t2 + 18t + 21 Reorder the terms: 35 = 21 + 18t + -3t2 Solving 35 = 21 + 18t + -3t2 Solving for variable 't'. Combine like terms: 35 + -21 = 14 14 + -18t + 3t2 = 21 + 18t + -3t2 + -21 + -18t + 3t2 Reorder the terms: 14 + -18t + 3t2 = 21 + -21 + 18t + -18t + -3t2 + 3t2 Combine like terms: 21 + -21 = 0 14 + -18t + 3t2 = 0 + 18t + -18t + -3t2 + 3t2 14 + -18t + 3t2 = 18t + -18t + -3t2 + 3t2 Combine like terms: 18t + -18t = 0 14 + -18t + 3t2 = 0 + -3t2 + 3t2 14 + -18t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 14 + -18t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + -6t + t2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + -6t + -4.666666667 + t2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + -6t + t2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + -6t + t2 = 0 + -4.666666667 -6t + t2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 -6t + t2 = -4.666666667 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -4.666666667 + 9 Reorder the terms: 9 + -6t + t2 = -4.666666667 + 9 Combine like terms: -4.666666667 + 9 = 4.333333333 9 + -6t + t2 = 4.333333333 Factor a perfect square on the left side: (t + -3)(t + -3) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (t + -3) equal to 2.081665999 and -2.081665999.Subproblem 1
t + -3 = 2.081665999 Simplifying t + -3 = 2.081665999 Reorder the terms: -3 + t = 2.081665999 Solving -3 + t = 2.081665999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.081665999 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.081665999 + 3 t = 2.081665999 + 3 Combine like terms: 2.081665999 + 3 = 5.081665999 t = 5.081665999 Simplifying t = 5.081665999Subproblem 2
t + -3 = -2.081665999 Simplifying t + -3 = -2.081665999 Reorder the terms: -3 + t = -2.081665999 Solving -3 + t = -2.081665999 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.081665999 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.081665999 + 3 t = -2.081665999 + 3 Combine like terms: -2.081665999 + 3 = 0.918334001 t = 0.918334001 Simplifying t = 0.918334001Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.081665999, 0.918334001}
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