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Simplifying 13 = -1t2 + 2t + 35 Reorder the terms: 13 = 35 + 2t + -1t2 Solving 13 = 35 + 2t + -1t2 Solving for variable 't'. Combine like terms: 13 + -35 = -22 -22 + -2t + t2 = 35 + 2t + -1t2 + -35 + -2t + t2 Reorder the terms: -22 + -2t + t2 = 35 + -35 + 2t + -2t + -1t2 + t2 Combine like terms: 35 + -35 = 0 -22 + -2t + t2 = 0 + 2t + -2t + -1t2 + t2 -22 + -2t + t2 = 2t + -2t + -1t2 + t2 Combine like terms: 2t + -2t = 0 -22 + -2t + t2 = 0 + -1t2 + t2 -22 + -2t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -22 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -2t + 22 + t2 = 0 + 22 Reorder the terms: -22 + 22 + -2t + t2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -2t + t2 = 0 + 22 -2t + t2 = 0 + 22 Combine like terms: 0 + 22 = 22 -2t + t2 = 22 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 = 22 + 1 Reorder the terms: 1 + -2t + t2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + -2t + t2 = 23 Factor a perfect square on the left side: (t + -1)(t + -1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (t + -1) equal to 4.795831523 and -4.795831523.Subproblem 1
t + -1 = 4.795831523 Simplifying t + -1 = 4.795831523 Reorder the terms: -1 + t = 4.795831523 Solving -1 + t = 4.795831523 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 = 4.795831523 + 1 Combine like terms: -1 + 1 = 0 0 + t = 4.795831523 + 1 t = 4.795831523 + 1 Combine like terms: 4.795831523 + 1 = 5.795831523 t = 5.795831523 Simplifying t = 5.795831523Subproblem 2
t + -1 = -4.795831523 Simplifying t + -1 = -4.795831523 Reorder the terms: -1 + t = -4.795831523 Solving -1 + t = -4.795831523 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 = -4.795831523 + 1 Combine like terms: -1 + 1 = 0 0 + t = -4.795831523 + 1 t = -4.795831523 + 1 Combine like terms: -4.795831523 + 1 = -3.795831523 t = -3.795831523 Simplifying t = -3.795831523Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.795831523, -3.795831523}
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