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Simplifying t = -5t2 + 5t + 60 Reorder the terms: t = 60 + 5t + -5t2 Solving t = 60 + 5t + -5t2 Solving for variable 't'. Reorder the terms: -60 + t + -5t + 5t2 = 60 + 5t + -5t2 + -60 + -5t + 5t2 Combine like terms: t + -5t = -4t -60 + -4t + 5t2 = 60 + 5t + -5t2 + -60 + -5t + 5t2 Reorder the terms: -60 + -4t + 5t2 = 60 + -60 + 5t + -5t + -5t2 + 5t2 Combine like terms: 60 + -60 = 0 -60 + -4t + 5t2 = 0 + 5t + -5t + -5t2 + 5t2 -60 + -4t + 5t2 = 5t + -5t + -5t2 + 5t2 Combine like terms: 5t + -5t = 0 -60 + -4t + 5t2 = 0 + -5t2 + 5t2 -60 + -4t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -60 + -4t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -0.8t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.8t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -0.8t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.8t + t2 = 0 + 12 -0.8t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.8t + t2 = 12 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 12 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 12 + 0.16 Combine like terms: 12 + 0.16 = 12.16 0.16 + -0.8t + t2 = 12.16 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 12.16 Calculate the square root of the right side: 3.487119155 Break this problem into two subproblems by setting (t + -0.4) equal to 3.487119155 and -3.487119155.Subproblem 1
t + -0.4 = 3.487119155 Simplifying t + -0.4 = 3.487119155 Reorder the terms: -0.4 + t = 3.487119155 Solving -0.4 + t = 3.487119155 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 3.487119155 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 3.487119155 + 0.4 t = 3.487119155 + 0.4 Combine like terms: 3.487119155 + 0.4 = 3.887119155 t = 3.887119155 Simplifying t = 3.887119155Subproblem 2
t + -0.4 = -3.487119155 Simplifying t + -0.4 = -3.487119155 Reorder the terms: -0.4 + t = -3.487119155 Solving -0.4 + t = -3.487119155 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -3.487119155 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -3.487119155 + 0.4 t = -3.487119155 + 0.4 Combine like terms: -3.487119155 + 0.4 = -3.087119155 t = -3.087119155 Simplifying t = -3.087119155Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.887119155, -3.087119155}
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