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Simplifying 0 = -16t2 + 48t + 40 Reorder the terms: 0 = 40 + 48t + -16t2 Solving 0 = 40 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -48t + 16t2 = 40 + 48t + -16t2 + -40 + -48t + 16t2 Reorder the terms: -40 + -48t + 16t2 = 40 + -40 + 48t + -48t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -40 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -40 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -40 + -48t + 16t2 = 0 + -16t2 + 16t2 -40 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + -6t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -6t + 2t2)' equal to zero and attempt to solve: Simplifying -5 + -6t + 2t2 = 0 Solving -5 + -6t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3t + t2 = 0 + 2.5 -3t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3t + t2 = 2.5 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 = 2.5 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + -3t + t2 = 4.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (t + -1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
t + -1.5 = 2.179449472 Simplifying t + -1.5 = 2.179449472 Reorder the terms: -1.5 + t = 2.179449472 Solving -1.5 + t = 2.179449472 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 = 2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 2.179449472 + 1.5 t = 2.179449472 + 1.5 Combine like terms: 2.179449472 + 1.5 = 3.679449472 t = 3.679449472 Simplifying t = 3.679449472Subproblem 2
t + -1.5 = -2.179449472 Simplifying t + -1.5 = -2.179449472 Reorder the terms: -1.5 + t = -2.179449472 Solving -1.5 + t = -2.179449472 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 = -2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -2.179449472 + 1.5 t = -2.179449472 + 1.5 Combine like terms: -2.179449472 + 1.5 = -0.679449472 t = -0.679449472 Simplifying t = -0.679449472Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.679449472, -0.679449472}Solution
t = {3.679449472, -0.679449472}
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