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Simplifying 0 = -1t2 + 8t + 6 Reorder the terms: 0 = 6 + 8t + -1t2 Solving 0 = 6 + 8t + -1t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -8t + t2 = 6 + 8t + -1t2 + -6 + -8t + t2 Reorder the terms: -6 + -8t + t2 = 6 + -6 + 8t + -8t + -1t2 + t2 Combine like terms: 6 + -6 = 0 -6 + -8t + t2 = 0 + 8t + -8t + -1t2 + t2 -6 + -8t + t2 = 8t + -8t + -1t2 + t2 Combine like terms: 8t + -8t = 0 -6 + -8t + t2 = 0 + -1t2 + t2 -6 + -8t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -6 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -8t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + -8t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8t + t2 = 0 + 6 -8t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8t + t2 = 6 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 6 + 16 Reorder the terms: 16 + -8t + t2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + -8t + t2 = 22 Factor a perfect square on the left side: (t + -4)(t + -4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (t + -4) equal to 4.69041576 and -4.69041576.Subproblem 1
t + -4 = 4.69041576 Simplifying t + -4 = 4.69041576 Reorder the terms: -4 + t = 4.69041576 Solving -4 + t = 4.69041576 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.69041576 + 4 t = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 t = 8.69041576 Simplifying t = 8.69041576Subproblem 2
t + -4 = -4.69041576 Simplifying t + -4 = -4.69041576 Reorder the terms: -4 + t = -4.69041576 Solving -4 + t = -4.69041576 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.69041576 + 4 t = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 t = -0.69041576 Simplifying t = -0.69041576Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.69041576, -0.69041576}
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