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Simplifying 3t2 + -14t + 3 = 0 Reorder the terms: 3 + -14t + 3t2 = 0 Solving 3 + -14t + 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'. 1 + -4.666666667t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.666666667t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -4.666666667t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.666666667t + t2 = 0 + -1 -4.666666667t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.666666667t + t2 = -1 The t term is -4.666666667t. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667t + 5.444444448 + t2 = -1 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667t + t2 = -1 + 5.444444448 Combine like terms: -1 + 5.444444448 = 4.444444448 5.444444448 + -4.666666667t + t2 = 4.444444448 Factor a perfect square on the left side: (t + -2.333333334)(t + -2.333333334) = 4.444444448 Calculate the square root of the right side: 2.108185108 Break this problem into two subproblems by setting (t + -2.333333334) equal to 2.108185108 and -2.108185108.Subproblem 1
t + -2.333333334 = 2.108185108 Simplifying t + -2.333333334 = 2.108185108 Reorder the terms: -2.333333334 + t = 2.108185108 Solving -2.333333334 + t = 2.108185108 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + t = 2.108185108 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + t = 2.108185108 + 2.333333334 t = 2.108185108 + 2.333333334 Combine like terms: 2.108185108 + 2.333333334 = 4.441518442 t = 4.441518442 Simplifying t = 4.441518442Subproblem 2
t + -2.333333334 = -2.108185108 Simplifying t + -2.333333334 = -2.108185108 Reorder the terms: -2.333333334 + t = -2.108185108 Solving -2.333333334 + t = -2.108185108 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + t = -2.108185108 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + t = -2.108185108 + 2.333333334 t = -2.108185108 + 2.333333334 Combine like terms: -2.108185108 + 2.333333334 = 0.225148226 t = 0.225148226 Simplifying t = 0.225148226Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.441518442, 0.225148226}
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