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Simplifying t = -5t2 + 20t + 60 Reorder the terms: t = 60 + 20t + -5t2 Solving t = 60 + 20t + -5t2 Solving for variable 't'. Reorder the terms: -60 + t + -20t + 5t2 = 60 + 20t + -5t2 + -60 + -20t + 5t2 Combine like terms: t + -20t = -19t -60 + -19t + 5t2 = 60 + 20t + -5t2 + -60 + -20t + 5t2 Reorder the terms: -60 + -19t + 5t2 = 60 + -60 + 20t + -20t + -5t2 + 5t2 Combine like terms: 60 + -60 = 0 -60 + -19t + 5t2 = 0 + 20t + -20t + -5t2 + 5t2 -60 + -19t + 5t2 = 20t + -20t + -5t2 + 5t2 Combine like terms: 20t + -20t = 0 -60 + -19t + 5t2 = 0 + -5t2 + 5t2 -60 + -19t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -60 + -19t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -3.8t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -3.8t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -3.8t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3.8t + t2 = 0 + 12 -3.8t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3.8t + t2 = 12 The t term is -3.8t. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8t + 3.61 + t2 = 12 + 3.61 Reorder the terms: 3.61 + -3.8t + t2 = 12 + 3.61 Combine like terms: 12 + 3.61 = 15.61 3.61 + -3.8t + t2 = 15.61 Factor a perfect square on the left side: (t + -1.9)(t + -1.9) = 15.61 Calculate the square root of the right side: 3.950949253 Break this problem into two subproblems by setting (t + -1.9) equal to 3.950949253 and -3.950949253.Subproblem 1
t + -1.9 = 3.950949253 Simplifying t + -1.9 = 3.950949253 Reorder the terms: -1.9 + t = 3.950949253 Solving -1.9 + t = 3.950949253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + t = 3.950949253 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + t = 3.950949253 + 1.9 t = 3.950949253 + 1.9 Combine like terms: 3.950949253 + 1.9 = 5.850949253 t = 5.850949253 Simplifying t = 5.850949253Subproblem 2
t + -1.9 = -3.950949253 Simplifying t + -1.9 = -3.950949253 Reorder the terms: -1.9 + t = -3.950949253 Solving -1.9 + t = -3.950949253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + t = -3.950949253 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + t = -3.950949253 + 1.9 t = -3.950949253 + 1.9 Combine like terms: -3.950949253 + 1.9 = -2.050949253 t = -2.050949253 Simplifying t = -2.050949253Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.850949253, -2.050949253}
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