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Simplifying 0 = 16t2 + -48t + -290 Reorder the terms: 0 = -290 + -48t + 16t2 Solving 0 = -290 + -48t + 16t2 Solving for variable 't'. Combine like terms: 0 + 290 = 290 290 + 48t + -16t2 = -290 + -48t + 16t2 + 290 + 48t + -16t2 Reorder the terms: 290 + 48t + -16t2 = -290 + 290 + -48t + 48t + 16t2 + -16t2 Combine like terms: -290 + 290 = 0 290 + 48t + -16t2 = 0 + -48t + 48t + 16t2 + -16t2 290 + 48t + -16t2 = -48t + 48t + 16t2 + -16t2 Combine like terms: -48t + 48t = 0 290 + 48t + -16t2 = 0 + 16t2 + -16t2 290 + 48t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 290 + 48t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(145 + 24t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(145 + 24t + -8t2)' equal to zero and attempt to solve: Simplifying 145 + 24t + -8t2 = 0 Solving 145 + 24t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -18.125 + -3t + t2 = 0 Move the constant term to the right: Add '18.125' to each side of the equation. -18.125 + -3t + 18.125 + t2 = 0 + 18.125 Reorder the terms: -18.125 + 18.125 + -3t + t2 = 0 + 18.125 Combine like terms: -18.125 + 18.125 = 0.000 0.000 + -3t + t2 = 0 + 18.125 -3t + t2 = 0 + 18.125 Combine like terms: 0 + 18.125 = 18.125 -3t + t2 = 18.125 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 18.125 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 18.125 + 2.25 Combine like terms: 18.125 + 2.25 = 20.375 2.25 + -3t + t2 = 20.375 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 20.375 Calculate the square root of the right side: 4.513867521 Break this problem into two subproblems by setting (t + -1.5) equal to 4.513867521 and -4.513867521.Subproblem 1
t + -1.5 = 4.513867521 Simplifying t + -1.5 = 4.513867521 Reorder the terms: -1.5 + t = 4.513867521 Solving -1.5 + t = 4.513867521 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 4.513867521 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 4.513867521 + 1.5 t = 4.513867521 + 1.5 Combine like terms: 4.513867521 + 1.5 = 6.013867521 t = 6.013867521 Simplifying t = 6.013867521Subproblem 2
t + -1.5 = -4.513867521 Simplifying t + -1.5 = -4.513867521 Reorder the terms: -1.5 + t = -4.513867521 Solving -1.5 + t = -4.513867521 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -4.513867521 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -4.513867521 + 1.5 t = -4.513867521 + 1.5 Combine like terms: -4.513867521 + 1.5 = -3.013867521 t = -3.013867521 Simplifying t = -3.013867521Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.013867521, -3.013867521}Solution
t = {6.013867521, -3.013867521}
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