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Simplifying 150 = 15t2 + -100t Reorder the terms: 150 = -100t + 15t2 Solving 150 = -100t + 15t2 Solving for variable 't'. Reorder the terms: 150 + 100t + -15t2 = -100t + 100t + 15t2 + -15t2 Combine like terms: -100t + 100t = 0 150 + 100t + -15t2 = 0 + 15t2 + -15t2 150 + 100t + -15t2 = 15t2 + -15t2 Combine like terms: 15t2 + -15t2 = 0 150 + 100t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(30 + 20t + -3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(30 + 20t + -3t2)' equal to zero and attempt to solve: Simplifying 30 + 20t + -3t2 = 0 Solving 30 + 20t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + -6.666666667t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -6.666666667t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -6.666666667t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6.666666667t + t2 = 0 + 10 -6.666666667t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6.666666667t + t2 = 10 The t term is -6.666666667t. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667t + 11.11111112 + t2 = 10 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667t + t2 = 10 + 11.11111112 Combine like terms: 10 + 11.11111112 = 21.11111112 11.11111112 + -6.666666667t + t2 = 21.11111112 Factor a perfect square on the left side: (t + -3.333333334)(t + -3.333333334) = 21.11111112 Calculate the square root of the right side: 4.594682918 Break this problem into two subproblems by setting (t + -3.333333334) equal to 4.594682918 and -4.594682918.Subproblem 1
t + -3.333333334 = 4.594682918 Simplifying t + -3.333333334 = 4.594682918 Reorder the terms: -3.333333334 + t = 4.594682918 Solving -3.333333334 + t = 4.594682918 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + t = 4.594682918 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + t = 4.594682918 + 3.333333334 t = 4.594682918 + 3.333333334 Combine like terms: 4.594682918 + 3.333333334 = 7.928016252 t = 7.928016252 Simplifying t = 7.928016252Subproblem 2
t + -3.333333334 = -4.594682918 Simplifying t + -3.333333334 = -4.594682918 Reorder the terms: -3.333333334 + t = -4.594682918 Solving -3.333333334 + t = -4.594682918 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + t = -4.594682918 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + t = -4.594682918 + 3.333333334 t = -4.594682918 + 3.333333334 Combine like terms: -4.594682918 + 3.333333334 = -1.261349584 t = -1.261349584 Simplifying t = -1.261349584Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.928016252, -1.261349584}Solution
t = {7.928016252, -1.261349584}
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