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Simplifying 2.5t2 + 5t + 20 = 50 Reorder the terms: 20 + 5t + 2.5t2 = 50 Solving 20 + 5t + 2.5t2 = 50 Solving for variable 't'. Reorder the terms: 20 + -50 + 5t + 2.5t2 = 50 + -50 Combine like terms: 20 + -50 = -30 -30 + 5t + 2.5t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -30 + 5t + 2.5t2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -12 + 2t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 2t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + 2t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2t + t2 = 0 + 12 2t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 2t + t2 = 12 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 12 + 1 Reorder the terms: 1 + 2t + t2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + 2t + t2 = 13 Factor a perfect square on the left side: (t + 1)(t + 1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (t + 1) equal to 3.605551275 and -3.605551275.Subproblem 1
t + 1 = 3.605551275 Simplifying t + 1 = 3.605551275 Reorder the terms: 1 + t = 3.605551275 Solving 1 + t = 3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.605551275 + -1 t = 3.605551275 + -1 Combine like terms: 3.605551275 + -1 = 2.605551275 t = 2.605551275 Simplifying t = 2.605551275Subproblem 2
t + 1 = -3.605551275 Simplifying t + 1 = -3.605551275 Reorder the terms: 1 + t = -3.605551275 Solving 1 + t = -3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -3.605551275 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.605551275 + -1 t = -3.605551275 + -1 Combine like terms: -3.605551275 + -1 = -4.605551275 t = -4.605551275 Simplifying t = -4.605551275Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.605551275, -4.605551275}
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