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Simplifying 15 = -5t2 + 30t Reorder the terms: 15 = 30t + -5t2 Solving 15 = 30t + -5t2 Solving for variable 't'. Reorder the terms: 15 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 15 + -30t + 5t2 = 0 + -5t2 + 5t2 15 + -30t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 15 + -30t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -6t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -6t + t2)' equal to zero and attempt to solve: Simplifying 3 + -6t + t2 = 0 Solving 3 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -6t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6t + t2 = 0 + -3 -6t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6t + t2 = -3 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -3 + 9 Reorder the terms: 9 + -6t + t2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6t + t2 = 6 Factor a perfect square on the left side: (t + -3)(t + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
t + -3 = 2.449489743 Simplifying t + -3 = 2.449489743 Reorder the terms: -3 + t = 2.449489743 Solving -3 + t = 2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.449489743 + 3 t = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 t = 5.449489743 Simplifying t = 5.449489743Subproblem 2
t + -3 = -2.449489743 Simplifying t + -3 = -2.449489743 Reorder the terms: -3 + t = -2.449489743 Solving -3 + t = -2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.449489743 + 3 t = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 t = 0.550510257 Simplifying t = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.449489743, 0.550510257}Solution
t = {5.449489743, 0.550510257}
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