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Simplifying 2t2 + 7t + -20 = 0 Reorder the terms: -20 + 7t + 2t2 = 0 Solving -20 + 7t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 3.5t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 3.5t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + 3.5t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3.5t + t2 = 0 + 10 3.5t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 3.5t + t2 = 10 The t term is 3.5t. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5t + 3.0625 + t2 = 10 + 3.0625 Reorder the terms: 3.0625 + 3.5t + t2 = 10 + 3.0625 Combine like terms: 10 + 3.0625 = 13.0625 3.0625 + 3.5t + t2 = 13.0625 Factor a perfect square on the left side: (t + 1.75)(t + 1.75) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (t + 1.75) equal to 3.614208074 and -3.614208074.Subproblem 1
t + 1.75 = 3.614208074 Simplifying t + 1.75 = 3.614208074 Reorder the terms: 1.75 + t = 3.614208074 Solving 1.75 + t = 3.614208074 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + t = 3.614208074 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + t = 3.614208074 + -1.75 t = 3.614208074 + -1.75 Combine like terms: 3.614208074 + -1.75 = 1.864208074 t = 1.864208074 Simplifying t = 1.864208074Subproblem 2
t + 1.75 = -3.614208074 Simplifying t + 1.75 = -3.614208074 Reorder the terms: 1.75 + t = -3.614208074 Solving 1.75 + t = -3.614208074 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + t = -3.614208074 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + t = -3.614208074 + -1.75 t = -3.614208074 + -1.75 Combine like terms: -3.614208074 + -1.75 = -5.364208074 t = -5.364208074 Simplifying t = -5.364208074Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.864208074, -5.364208074}
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