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Simplifying 0 = -16t2 + 64t + 2 Reorder the terms: 0 = 2 + 64t + -16t2 Solving 0 = 2 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -64t + 16t2 = 2 + 64t + -16t2 + -2 + -64t + 16t2 Reorder the terms: -2 + -64t + 16t2 = 2 + -2 + 64t + -64t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -2 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -2 + -64t + 16t2 = 0 + -16t2 + 16t2 -2 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -32t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -32t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + -32t + 8t2 = 0 Solving -1 + -32t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -4t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -4t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -4t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -4t + t2 = 0 + 0.125 -4t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -4t + t2 = 0.125 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 = 0.125 + 4 Reorder the terms: 4 + -4t + t2 = 0.125 + 4 Combine like terms: 0.125 + 4 = 4.125 4 + -4t + t2 = 4.125 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.125 Calculate the square root of the right side: 2.031009601 Break this problem into two subproblems by setting (t + -2) equal to 2.031009601 and -2.031009601.Subproblem 1
t + -2 = 2.031009601 Simplifying t + -2 = 2.031009601 Reorder the terms: -2 + t = 2.031009601 Solving -2 + t = 2.031009601 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 = 2.031009601 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.031009601 + 2 t = 2.031009601 + 2 Combine like terms: 2.031009601 + 2 = 4.031009601 t = 4.031009601 Simplifying t = 4.031009601Subproblem 2
t + -2 = -2.031009601 Simplifying t + -2 = -2.031009601 Reorder the terms: -2 + t = -2.031009601 Solving -2 + t = -2.031009601 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 = -2.031009601 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.031009601 + 2 t = -2.031009601 + 2 Combine like terms: -2.031009601 + 2 = -0.031009601 t = -0.031009601 Simplifying t = -0.031009601Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.031009601, -0.031009601}Solution
t = {4.031009601, -0.031009601}
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