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Simplifying 0 = -16t2 + 2t + 10 Reorder the terms: 0 = 10 + 2t + -16t2 Solving 0 = 10 + 2t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -2t + 16t2 = 10 + 2t + -16t2 + -10 + -2t + 16t2 Reorder the terms: -10 + -2t + 16t2 = 10 + -10 + 2t + -2t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + -2t + 16t2 = 0 + 2t + -2t + -16t2 + 16t2 -10 + -2t + 16t2 = 2t + -2t + -16t2 + 16t2 Combine like terms: 2t + -2t = 0 -10 + -2t + 16t2 = 0 + -16t2 + 16t2 -10 + -2t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -2t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -1t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1t + 8t2)' equal to zero and attempt to solve: Simplifying -5 + -1t + 8t2 = 0 Solving -5 + -1t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -0.125t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.125t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.125t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.125t + t2 = 0 + 0.625 -0.125t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.125t + t2 = 0.625 The t term is -0.125t. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125t + 0.00390625 + t2 = 0.625 + 0.00390625 Reorder the terms: 0.00390625 + -0.125t + t2 = 0.625 + 0.00390625 Combine like terms: 0.625 + 0.00390625 = 0.62890625 0.00390625 + -0.125t + t2 = 0.62890625 Factor a perfect square on the left side: (t + -0.0625)(t + -0.0625) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (t + -0.0625) equal to 0.793036096 and -0.793036096.Subproblem 1
t + -0.0625 = 0.793036096 Simplifying t + -0.0625 = 0.793036096 Reorder the terms: -0.0625 + t = 0.793036096 Solving -0.0625 + t = 0.793036096 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + t = 0.793036096 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + t = 0.793036096 + 0.0625 t = 0.793036096 + 0.0625 Combine like terms: 0.793036096 + 0.0625 = 0.855536096 t = 0.855536096 Simplifying t = 0.855536096Subproblem 2
t + -0.0625 = -0.793036096 Simplifying t + -0.0625 = -0.793036096 Reorder the terms: -0.0625 + t = -0.793036096 Solving -0.0625 + t = -0.793036096 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + t = -0.793036096 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + t = -0.793036096 + 0.0625 t = -0.793036096 + 0.0625 Combine like terms: -0.793036096 + 0.0625 = -0.730536096 t = -0.730536096 Simplifying t = -0.730536096Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.855536096, -0.730536096}Solution
t = {0.855536096, -0.730536096}
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