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Simplifying t2 + 20t + -94.10 = 0 Reorder the terms: -94.10 + 20t + t2 = 0 Solving -94.10 + 20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '94.10' to each side of the equation. -94.10 + 20t + 94.10 + t2 = 0 + 94.10 Reorder the terms: -94.10 + 94.10 + 20t + t2 = 0 + 94.10 Combine like terms: -94.10 + 94.10 = 0.00 0.00 + 20t + t2 = 0 + 94.10 20t + t2 = 0 + 94.10 Combine like terms: 0 + 94.10 = 94.1 20t + t2 = 94.1 The t term is 20t. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t + 100 + t2 = 94.1 + 100 Reorder the terms: 100 + 20t + t2 = 94.1 + 100 Combine like terms: 94.1 + 100 = 194.1 100 + 20t + t2 = 194.1 Factor a perfect square on the left side: (t + 10)(t + 10) = 194.1 Calculate the square root of the right side: 13.931977605 Break this problem into two subproblems by setting (t + 10) equal to 13.931977605 and -13.931977605.Subproblem 1
t + 10 = 13.931977605 Simplifying t + 10 = 13.931977605 Reorder the terms: 10 + t = 13.931977605 Solving 10 + t = 13.931977605 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 13.931977605 + -10 Combine like terms: 10 + -10 = 0 0 + t = 13.931977605 + -10 t = 13.931977605 + -10 Combine like terms: 13.931977605 + -10 = 3.931977605 t = 3.931977605 Simplifying t = 3.931977605Subproblem 2
t + 10 = -13.931977605 Simplifying t + 10 = -13.931977605 Reorder the terms: 10 + t = -13.931977605 Solving 10 + t = -13.931977605 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = -13.931977605 + -10 Combine like terms: 10 + -10 = 0 0 + t = -13.931977605 + -10 t = -13.931977605 + -10 Combine like terms: -13.931977605 + -10 = -23.931977605 t = -23.931977605 Simplifying t = -23.931977605Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.931977605, -23.931977605}
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