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Simplifying 5t2 + 8t = 30 Reorder the terms: 8t + 5t2 = 30 Solving 8t + 5t2 = 30 Solving for variable 't'. Reorder the terms: -30 + 8t + 5t2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 8t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + 1.6t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.6t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 1.6t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.6t + t2 = 0 + 6 1.6t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.6t + t2 = 6 The t term is 1.6t. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6t + 0.64 + t2 = 6 + 0.64 Reorder the terms: 0.64 + 1.6t + t2 = 6 + 0.64 Combine like terms: 6 + 0.64 = 6.64 0.64 + 1.6t + t2 = 6.64 Factor a perfect square on the left side: (t + 0.8)(t + 0.8) = 6.64 Calculate the square root of the right side: 2.576819745 Break this problem into two subproblems by setting (t + 0.8) equal to 2.576819745 and -2.576819745.Subproblem 1
t + 0.8 = 2.576819745 Simplifying t + 0.8 = 2.576819745 Reorder the terms: 0.8 + t = 2.576819745 Solving 0.8 + t = 2.576819745 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = 2.576819745 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = 2.576819745 + -0.8 t = 2.576819745 + -0.8 Combine like terms: 2.576819745 + -0.8 = 1.776819745 t = 1.776819745 Simplifying t = 1.776819745Subproblem 2
t + 0.8 = -2.576819745 Simplifying t + 0.8 = -2.576819745 Reorder the terms: 0.8 + t = -2.576819745 Solving 0.8 + t = -2.576819745 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + t = -2.576819745 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + t = -2.576819745 + -0.8 t = -2.576819745 + -0.8 Combine like terms: -2.576819745 + -0.8 = -3.376819745 t = -3.376819745 Simplifying t = -3.376819745Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.776819745, -3.376819745}
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