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Simplifying 0 = -16t2 + 48t + 768 Reorder the terms: 0 = 768 + 48t + -16t2 Solving 0 = 768 + 48t + -16t2 Solving for variable 't'. Combine like terms: 0 + -768 = -768 -768 + -48t + 16t2 = 768 + 48t + -16t2 + -768 + -48t + 16t2 Reorder the terms: -768 + -48t + 16t2 = 768 + -768 + 48t + -48t + -16t2 + 16t2 Combine like terms: 768 + -768 = 0 -768 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -768 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -768 + -48t + 16t2 = 0 + -16t2 + 16t2 -768 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -768 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-48 + -3t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-48 + -3t + t2)' equal to zero and attempt to solve: Simplifying -48 + -3t + t2 = 0 Solving -48 + -3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -3t + 48 + t2 = 0 + 48 Reorder the terms: -48 + 48 + -3t + t2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -3t + t2 = 0 + 48 -3t + t2 = 0 + 48 Combine like terms: 0 + 48 = 48 -3t + t2 = 48 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 = 48 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 48 + 2.25 Combine like terms: 48 + 2.25 = 50.25 2.25 + -3t + t2 = 50.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (t + -1.5) equal to 7.088723439 and -7.088723439.Subproblem 1
t + -1.5 = 7.088723439 Simplifying t + -1.5 = 7.088723439 Reorder the terms: -1.5 + t = 7.088723439 Solving -1.5 + t = 7.088723439 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 = 7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 7.088723439 + 1.5 t = 7.088723439 + 1.5 Combine like terms: 7.088723439 + 1.5 = 8.588723439 t = 8.588723439 Simplifying t = 8.588723439Subproblem 2
t + -1.5 = -7.088723439 Simplifying t + -1.5 = -7.088723439 Reorder the terms: -1.5 + t = -7.088723439 Solving -1.5 + t = -7.088723439 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 = -7.088723439 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -7.088723439 + 1.5 t = -7.088723439 + 1.5 Combine like terms: -7.088723439 + 1.5 = -5.588723439 t = -5.588723439 Simplifying t = -5.588723439Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.588723439, -5.588723439}Solution
t = {8.588723439, -5.588723439}
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