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Simplifying 3t2 + -44t + 45 = 0 Reorder the terms: 45 + -44t + 3t2 = 0 Solving 45 + -44t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15 + -14.66666667t + t2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -14.66666667t + -15 + t2 = 0 + -15 Reorder the terms: 15 + -15 + -14.66666667t + t2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -14.66666667t + t2 = 0 + -15 -14.66666667t + t2 = 0 + -15 Combine like terms: 0 + -15 = -15 -14.66666667t + t2 = -15 The t term is -14.66666667t. Take half its coefficient (-7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. -14.66666667t + 53.77777780 + t2 = -15 + 53.77777780 Reorder the terms: 53.77777780 + -14.66666667t + t2 = -15 + 53.77777780 Combine like terms: -15 + 53.77777780 = 38.7777778 53.77777780 + -14.66666667t + t2 = 38.7777778 Factor a perfect square on the left side: (t + -7.333333335)(t + -7.333333335) = 38.7777778 Calculate the square root of the right side: 6.227180566 Break this problem into two subproblems by setting (t + -7.333333335) equal to 6.227180566 and -6.227180566.Subproblem 1
t + -7.333333335 = 6.227180566 Simplifying t + -7.333333335 = 6.227180566 Reorder the terms: -7.333333335 + t = 6.227180566 Solving -7.333333335 + t = 6.227180566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + t = 6.227180566 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + t = 6.227180566 + 7.333333335 t = 6.227180566 + 7.333333335 Combine like terms: 6.227180566 + 7.333333335 = 13.560513901 t = 13.560513901 Simplifying t = 13.560513901Subproblem 2
t + -7.333333335 = -6.227180566 Simplifying t + -7.333333335 = -6.227180566 Reorder the terms: -7.333333335 + t = -6.227180566 Solving -7.333333335 + t = -6.227180566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + t = -6.227180566 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + t = -6.227180566 + 7.333333335 t = -6.227180566 + 7.333333335 Combine like terms: -6.227180566 + 7.333333335 = 1.106152769 t = 1.106152769 Simplifying t = 1.106152769Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.560513901, 1.106152769}
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