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Simplifying 150 = -16t2 + 120t + 4 Reorder the terms: 150 = 4 + 120t + -16t2 Solving 150 = 4 + 120t + -16t2 Solving for variable 't'. Combine like terms: 150 + -4 = 146 146 + -120t + 16t2 = 4 + 120t + -16t2 + -4 + -120t + 16t2 Reorder the terms: 146 + -120t + 16t2 = 4 + -4 + 120t + -120t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 146 + -120t + 16t2 = 0 + 120t + -120t + -16t2 + 16t2 146 + -120t + 16t2 = 120t + -120t + -16t2 + 16t2 Combine like terms: 120t + -120t = 0 146 + -120t + 16t2 = 0 + -16t2 + 16t2 146 + -120t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 146 + -120t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(73 + -60t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(73 + -60t + 8t2)' equal to zero and attempt to solve: Simplifying 73 + -60t + 8t2 = 0 Solving 73 + -60t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 9.125 + -7.5t + t2 = 0 Move the constant term to the right: Add '-9.125' to each side of the equation. 9.125 + -7.5t + -9.125 + t2 = 0 + -9.125 Reorder the terms: 9.125 + -9.125 + -7.5t + t2 = 0 + -9.125 Combine like terms: 9.125 + -9.125 = 0.000 0.000 + -7.5t + t2 = 0 + -9.125 -7.5t + t2 = 0 + -9.125 Combine like terms: 0 + -9.125 = -9.125 -7.5t + t2 = -9.125 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = -9.125 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = -9.125 + 14.0625 Combine like terms: -9.125 + 14.0625 = 4.9375 14.0625 + -7.5t + t2 = 4.9375 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 4.9375 Calculate the square root of the right side: 2.222048604 Break this problem into two subproblems by setting (t + -3.75) equal to 2.222048604 and -2.222048604.Subproblem 1
t + -3.75 = 2.222048604 Simplifying t + -3.75 = 2.222048604 Reorder the terms: -3.75 + t = 2.222048604 Solving -3.75 + t = 2.222048604 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 2.222048604 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 2.222048604 + 3.75 t = 2.222048604 + 3.75 Combine like terms: 2.222048604 + 3.75 = 5.972048604 t = 5.972048604 Simplifying t = 5.972048604Subproblem 2
t + -3.75 = -2.222048604 Simplifying t + -3.75 = -2.222048604 Reorder the terms: -3.75 + t = -2.222048604 Solving -3.75 + t = -2.222048604 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -2.222048604 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -2.222048604 + 3.75 t = -2.222048604 + 3.75 Combine like terms: -2.222048604 + 3.75 = 1.527951396 t = 1.527951396 Simplifying t = 1.527951396Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.972048604, 1.527951396}Solution
t = {5.972048604, 1.527951396}
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