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Simplifying 0 = -16t2 + 64t + 18 Reorder the terms: 0 = 18 + 64t + -16t2 Solving 0 = 18 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -18 = -18 -18 + -64t + 16t2 = 18 + 64t + -16t2 + -18 + -64t + 16t2 Reorder the terms: -18 + -64t + 16t2 = 18 + -18 + 64t + -64t + -16t2 + 16t2 Combine like terms: 18 + -18 = 0 -18 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -18 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -18 + -64t + 16t2 = 0 + -16t2 + 16t2 -18 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -18 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -32t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -32t + 8t2)' equal to zero and attempt to solve: Simplifying -9 + -32t + 8t2 = 0 Solving -9 + -32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -4t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -4t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -4t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -4t + t2 = 0 + 1.125 -4t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -4t + t2 = 1.125 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 1.125 + 4 Reorder the terms: 4 + -4t + t2 = 1.125 + 4 Combine like terms: 1.125 + 4 = 5.125 4 + -4t + t2 = 5.125 Factor a perfect square on the left side: (t + -2)(t + -2) = 5.125 Calculate the square root of the right side: 2.263846285 Break this problem into two subproblems by setting (t + -2) equal to 2.263846285 and -2.263846285.Subproblem 1
t + -2 = 2.263846285 Simplifying t + -2 = 2.263846285 Reorder the terms: -2 + t = 2.263846285 Solving -2 + t = 2.263846285 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.263846285 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.263846285 + 2 t = 2.263846285 + 2 Combine like terms: 2.263846285 + 2 = 4.263846285 t = 4.263846285 Simplifying t = 4.263846285Subproblem 2
t + -2 = -2.263846285 Simplifying t + -2 = -2.263846285 Reorder the terms: -2 + t = -2.263846285 Solving -2 + t = -2.263846285 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.263846285 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.263846285 + 2 t = -2.263846285 + 2 Combine like terms: -2.263846285 + 2 = -0.263846285 t = -0.263846285 Simplifying t = -0.263846285Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.263846285, -0.263846285}Solution
t = {4.263846285, -0.263846285}
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