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Simplifying 8 = -0.0417t2 + -0.08333t + 10 Reorder the terms: 8 = 10 + -0.08333t + -0.0417t2 Solving 8 = 10 + -0.08333t + -0.0417t2 Solving for variable 't'. Combine like terms: 8 + -10 = -2 -2 + 0.08333t + 0.0417t2 = 10 + -0.08333t + -0.0417t2 + -10 + 0.08333t + 0.0417t2 Reorder the terms: -2 + 0.08333t + 0.0417t2 = 10 + -10 + -0.08333t + 0.08333t + -0.0417t2 + 0.0417t2 Combine like terms: 10 + -10 = 0 -2 + 0.08333t + 0.0417t2 = 0 + -0.08333t + 0.08333t + -0.0417t2 + 0.0417t2 -2 + 0.08333t + 0.0417t2 = -0.08333t + 0.08333t + -0.0417t2 + 0.0417t2 Combine like terms: -0.08333t + 0.08333t = 0.00000 -2 + 0.08333t + 0.0417t2 = 0.00000 + -0.0417t2 + 0.0417t2 -2 + 0.08333t + 0.0417t2 = -0.0417t2 + 0.0417t2 Combine like terms: -0.0417t2 + 0.0417t2 = 0.0000 -2 + 0.08333t + 0.0417t2 = 0.0000 Begin completing the square. Divide all terms by 0.0417 the coefficient of the squared term: Divide each side by '0.0417'. -47.9616307 + 1.998321343t + t2 = 0 Move the constant term to the right: Add '47.9616307' to each side of the equation. -47.9616307 + 1.998321343t + 47.9616307 + t2 = 0 + 47.9616307 Reorder the terms: -47.9616307 + 47.9616307 + 1.998321343t + t2 = 0 + 47.9616307 Combine like terms: -47.9616307 + 47.9616307 = 0.0000000 0.0000000 + 1.998321343t + t2 = 0 + 47.9616307 1.998321343t + t2 = 0 + 47.9616307 Combine like terms: 0 + 47.9616307 = 47.9616307 1.998321343t + t2 = 47.9616307 The t term is 1.998321343t. Take half its coefficient (0.9991606715). Square it (0.9983220475) and add it to both sides. Add '0.9983220475' to each side of the equation. 1.998321343t + 0.9983220475 + t2 = 47.9616307 + 0.9983220475 Reorder the terms: 0.9983220475 + 1.998321343t + t2 = 47.9616307 + 0.9983220475 Combine like terms: 47.9616307 + 0.9983220475 = 48.9599527475 0.9983220475 + 1.998321343t + t2 = 48.9599527475 Factor a perfect square on the left side: (t + 0.9991606715)(t + 0.9991606715) = 48.9599527475 Calculate the square root of the right side: 6.997138897 Break this problem into two subproblems by setting (t + 0.9991606715) equal to 6.997138897 and -6.997138897.Subproblem 1
t + 0.9991606715 = 6.997138897 Simplifying t + 0.9991606715 = 6.997138897 Reorder the terms: 0.9991606715 + t = 6.997138897 Solving 0.9991606715 + t = 6.997138897 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9991606715' to each side of the equation. 0.9991606715 + -0.9991606715 + t = 6.997138897 + -0.9991606715 Combine like terms: 0.9991606715 + -0.9991606715 = 0.0000000000 0.0000000000 + t = 6.997138897 + -0.9991606715 t = 6.997138897 + -0.9991606715 Combine like terms: 6.997138897 + -0.9991606715 = 5.9979782255 t = 5.9979782255 Simplifying t = 5.9979782255Subproblem 2
t + 0.9991606715 = -6.997138897 Simplifying t + 0.9991606715 = -6.997138897 Reorder the terms: 0.9991606715 + t = -6.997138897 Solving 0.9991606715 + t = -6.997138897 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9991606715' to each side of the equation. 0.9991606715 + -0.9991606715 + t = -6.997138897 + -0.9991606715 Combine like terms: 0.9991606715 + -0.9991606715 = 0.0000000000 0.0000000000 + t = -6.997138897 + -0.9991606715 t = -6.997138897 + -0.9991606715 Combine like terms: -6.997138897 + -0.9991606715 = -7.9962995685 t = -7.9962995685 Simplifying t = -7.9962995685Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.9979782255, -7.9962995685}
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