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Simplifying 0 = -16t2 + 48t + 18 Reorder the terms: 0 = 18 + 48t + -16t2 Solving 0 = 18 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + -18 = -18 -18 + -48t + 16t2 = 18 + 48t + -16t2 + -18 + -48t + 16t2 Reorder the terms: -18 + -48t + 16t2 = 18 + -18 + 48t + -48t + -16t2 + 16t2 Combine like terms: 18 + -18 = 0 -18 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -18 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -18 + -48t + 16t2 = 0 + -16t2 + 16t2 -18 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -18 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -24t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -24t + 8t2)' equal to zero and attempt to solve: Simplifying -9 + -24t + 8t2 = 0 Solving -9 + -24t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -3t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -3t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -3t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -3t + t2 = 0 + 1.125 -3t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -3t + t2 = 1.125 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 = 1.125 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 1.125 + 2.25 Combine like terms: 1.125 + 2.25 = 3.375 2.25 + -3t + t2 = 3.375 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 3.375 Calculate the square root of the right side: 1.837117307 Break this problem into two subproblems by setting (t + -1.5) equal to 1.837117307 and -1.837117307.Subproblem 1
t + -1.5 = 1.837117307 Simplifying t + -1.5 = 1.837117307 Reorder the terms: -1.5 + t = 1.837117307 Solving -1.5 + t = 1.837117307 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 = 1.837117307 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.837117307 + 1.5 t = 1.837117307 + 1.5 Combine like terms: 1.837117307 + 1.5 = 3.337117307 t = 3.337117307 Simplifying t = 3.337117307Subproblem 2
t + -1.5 = -1.837117307 Simplifying t + -1.5 = -1.837117307 Reorder the terms: -1.5 + t = -1.837117307 Solving -1.5 + t = -1.837117307 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 = -1.837117307 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.837117307 + 1.5 t = -1.837117307 + 1.5 Combine like terms: -1.837117307 + 1.5 = -0.337117307 t = -0.337117307 Simplifying t = -0.337117307Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.337117307, -0.337117307}Solution
t = {3.337117307, -0.337117307}
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