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Simplifying 0.000144t2 + -0.0122t + 0.0613 = 0 Reorder the terms: 0.0613 + -0.0122t + 0.000144t2 = 0 Solving 0.0613 + -0.0122t + 0.000144t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.000144 the coefficient of the squared term: Divide each side by '0.000144'. 425.6944444 + -84.72222222t + t2 = 0 Move the constant term to the right: Add '-425.6944444' to each side of the equation. 425.6944444 + -84.72222222t + -425.6944444 + t2 = 0 + -425.6944444 Reorder the terms: 425.6944444 + -425.6944444 + -84.72222222t + t2 = 0 + -425.6944444 Combine like terms: 425.6944444 + -425.6944444 = 0.0000000 0.0000000 + -84.72222222t + t2 = 0 + -425.6944444 -84.72222222t + t2 = 0 + -425.6944444 Combine like terms: 0 + -425.6944444 = -425.6944444 -84.72222222t + t2 = -425.6944444 The t term is -84.72222222t. Take half its coefficient (-42.36111111). Square it (1794.463734) and add it to both sides. Add '1794.463734' to each side of the equation. -84.72222222t + 1794.463734 + t2 = -425.6944444 + 1794.463734 Reorder the terms: 1794.463734 + -84.72222222t + t2 = -425.6944444 + 1794.463734 Combine like terms: -425.6944444 + 1794.463734 = 1368.7692896 1794.463734 + -84.72222222t + t2 = 1368.7692896 Factor a perfect square on the left side: (t + -42.36111111)(t + -42.36111111) = 1368.7692896 Calculate the square root of the right side: 36.996882161 Break this problem into two subproblems by setting (t + -42.36111111) equal to 36.996882161 and -36.996882161.Subproblem 1
t + -42.36111111 = 36.996882161 Simplifying t + -42.36111111 = 36.996882161 Reorder the terms: -42.36111111 + t = 36.996882161 Solving -42.36111111 + t = 36.996882161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '42.36111111' to each side of the equation. -42.36111111 + 42.36111111 + t = 36.996882161 + 42.36111111 Combine like terms: -42.36111111 + 42.36111111 = 0.00000000 0.00000000 + t = 36.996882161 + 42.36111111 t = 36.996882161 + 42.36111111 Combine like terms: 36.996882161 + 42.36111111 = 79.357993271 t = 79.357993271 Simplifying t = 79.357993271Subproblem 2
t + -42.36111111 = -36.996882161 Simplifying t + -42.36111111 = -36.996882161 Reorder the terms: -42.36111111 + t = -36.996882161 Solving -42.36111111 + t = -36.996882161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '42.36111111' to each side of the equation. -42.36111111 + 42.36111111 + t = -36.996882161 + 42.36111111 Combine like terms: -42.36111111 + 42.36111111 = 0.00000000 0.00000000 + t = -36.996882161 + 42.36111111 t = -36.996882161 + 42.36111111 Combine like terms: -36.996882161 + 42.36111111 = 5.364228949 t = 5.364228949 Simplifying t = 5.364228949Solution
The solution to the problem is based on the solutions from the subproblems. t = {79.357993271, 5.364228949}
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