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Simplifying 0 = -16t2 + 48t + 20 Reorder the terms: 0 = 20 + 48t + -16t2 Solving 0 = 20 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + -48t + 16t2 = 20 + 48t + -16t2 + -20 + -48t + 16t2 Reorder the terms: -20 + -48t + 16t2 = 20 + -20 + 48t + -48t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -20 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -20 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -20 + -48t + 16t2 = 0 + -16t2 + 16t2 -20 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -12t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -12t + 4t2)' equal to zero and attempt to solve: Simplifying -5 + -12t + 4t2 = 0 Solving -5 + -12t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -3t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3t + t2 = 0 + 1.25 -3t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3t + t2 = 1.25 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 = 1.25 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 1.25 + 2.25 Combine like terms: 1.25 + 2.25 = 3.5 2.25 + -3t + t2 = 3.5 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (t + -1.5) equal to 1.870828693 and -1.870828693.Subproblem 1
t + -1.5 = 1.870828693 Simplifying t + -1.5 = 1.870828693 Reorder the terms: -1.5 + t = 1.870828693 Solving -1.5 + t = 1.870828693 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 = 1.870828693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.870828693 + 1.5 t = 1.870828693 + 1.5 Combine like terms: 1.870828693 + 1.5 = 3.370828693 t = 3.370828693 Simplifying t = 3.370828693Subproblem 2
t + -1.5 = -1.870828693 Simplifying t + -1.5 = -1.870828693 Reorder the terms: -1.5 + t = -1.870828693 Solving -1.5 + t = -1.870828693 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 = -1.870828693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.870828693 + 1.5 t = -1.870828693 + 1.5 Combine like terms: -1.870828693 + 1.5 = -0.370828693 t = -0.370828693 Simplifying t = -0.370828693Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.370828693, -0.370828693}Solution
t = {3.370828693, -0.370828693}
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