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Simplifying 15 = 40t + -15t2 Solving 15 = 40t + -15t2 Solving for variable 't'. Reorder the terms: 15 + -40t + 15t2 = 40t + -40t + -15t2 + 15t2 Combine like terms: 40t + -40t = 0 15 + -40t + 15t2 = 0 + -15t2 + 15t2 15 + -40t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 15 + -40t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -8t + 3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -8t + 3t2)' equal to zero and attempt to solve: Simplifying 3 + -8t + 3t2 = 0 Solving 3 + -8t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -2.666666667t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.666666667t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -2.666666667t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.666666667t + t2 = 0 + -1 -2.666666667t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.666666667t + t2 = -1 The t term is -2.666666667t. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667t + 1.777777780 + t2 = -1 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667t + t2 = -1 + 1.777777780 Combine like terms: -1 + 1.777777780 = 0.77777778 1.777777780 + -2.666666667t + t2 = 0.77777778 Factor a perfect square on the left side: (t + -1.333333334)(t + -1.333333334) = 0.77777778 Calculate the square root of the right side: 0.881917105 Break this problem into two subproblems by setting (t + -1.333333334) equal to 0.881917105 and -0.881917105.Subproblem 1
t + -1.333333334 = 0.881917105 Simplifying t + -1.333333334 = 0.881917105 Reorder the terms: -1.333333334 + t = 0.881917105 Solving -1.333333334 + t = 0.881917105 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + t = 0.881917105 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = 0.881917105 + 1.333333334 t = 0.881917105 + 1.333333334 Combine like terms: 0.881917105 + 1.333333334 = 2.215250439 t = 2.215250439 Simplifying t = 2.215250439Subproblem 2
t + -1.333333334 = -0.881917105 Simplifying t + -1.333333334 = -0.881917105 Reorder the terms: -1.333333334 + t = -0.881917105 Solving -1.333333334 + t = -0.881917105 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + t = -0.881917105 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = -0.881917105 + 1.333333334 t = -0.881917105 + 1.333333334 Combine like terms: -0.881917105 + 1.333333334 = 0.451416229 t = 0.451416229 Simplifying t = 0.451416229Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.215250439, 0.451416229}Solution
t = {2.215250439, 0.451416229}
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