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Simplifying (0.0895) * t2 + -4.7t + 42 = 0 Reorder the terms: 42 + -4.7t + 0.0895t2 = 0 Solving 42 + -4.7t + 0.0895t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0895 the coefficient of the squared term: Divide each side by '0.0895'. 469.273743 + -52.51396648t + t2 = 0 Move the constant term to the right: Add '-469.273743' to each side of the equation. 469.273743 + -52.51396648t + -469.273743 + t2 = 0 + -469.273743 Reorder the terms: 469.273743 + -469.273743 + -52.51396648t + t2 = 0 + -469.273743 Combine like terms: 469.273743 + -469.273743 = 0.000000 0.000000 + -52.51396648t + t2 = 0 + -469.273743 -52.51396648t + t2 = 0 + -469.273743 Combine like terms: 0 + -469.273743 = -469.273743 -52.51396648t + t2 = -469.273743 The t term is -52.51396648t. Take half its coefficient (-26.25698324). Square it (689.4291689) and add it to both sides. Add '689.4291689' to each side of the equation. -52.51396648t + 689.4291689 + t2 = -469.273743 + 689.4291689 Reorder the terms: 689.4291689 + -52.51396648t + t2 = -469.273743 + 689.4291689 Combine like terms: -469.273743 + 689.4291689 = 220.1554259 689.4291689 + -52.51396648t + t2 = 220.1554259 Factor a perfect square on the left side: (t + -26.25698324)(t + -26.25698324) = 220.1554259 Calculate the square root of the right side: 14.837635455 Break this problem into two subproblems by setting (t + -26.25698324) equal to 14.837635455 and -14.837635455.Subproblem 1
t + -26.25698324 = 14.837635455 Simplifying t + -26.25698324 = 14.837635455 Reorder the terms: -26.25698324 + t = 14.837635455 Solving -26.25698324 + t = 14.837635455 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '26.25698324' to each side of the equation. -26.25698324 + 26.25698324 + t = 14.837635455 + 26.25698324 Combine like terms: -26.25698324 + 26.25698324 = 0.00000000 0.00000000 + t = 14.837635455 + 26.25698324 t = 14.837635455 + 26.25698324 Combine like terms: 14.837635455 + 26.25698324 = 41.094618695 t = 41.094618695 Simplifying t = 41.094618695Subproblem 2
t + -26.25698324 = -14.837635455 Simplifying t + -26.25698324 = -14.837635455 Reorder the terms: -26.25698324 + t = -14.837635455 Solving -26.25698324 + t = -14.837635455 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '26.25698324' to each side of the equation. -26.25698324 + 26.25698324 + t = -14.837635455 + 26.25698324 Combine like terms: -26.25698324 + 26.25698324 = 0.00000000 0.00000000 + t = -14.837635455 + 26.25698324 t = -14.837635455 + 26.25698324 Combine like terms: -14.837635455 + 26.25698324 = 11.419347785 t = 11.419347785 Simplifying t = 11.419347785Solution
The solution to the problem is based on the solutions from the subproblems. t = {41.094618695, 11.419347785}
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