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Simplifying -16t3 + 7t2 + 2t = 0 Reorder the terms: 2t + 7t2 + -16t3 = 0 Solving 2t + 7t2 + -16t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(2 + 7t + -16t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(2 + 7t + -16t2)' equal to zero and attempt to solve: Simplifying 2 + 7t + -16t2 = 0 Solving 2 + 7t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.125 + -0.4375t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.4375t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.4375t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.4375t + t2 = 0 + 0.125 -0.4375t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.4375t + t2 = 0.125 The t term is -0.4375t. Take half its coefficient (-0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. -0.4375t + 0.0478515625 + t2 = 0.125 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375t + t2 = 0.125 + 0.0478515625 Combine like terms: 0.125 + 0.0478515625 = 0.1728515625 0.0478515625 + -0.4375t + t2 = 0.1728515625 Factor a perfect square on the left side: (t + -0.21875)(t + -0.21875) = 0.1728515625 Calculate the square root of the right side: 0.415754209 Break this problem into two subproblems by setting (t + -0.21875) equal to 0.415754209 and -0.415754209.Subproblem 1
t + -0.21875 = 0.415754209 Simplifying t + -0.21875 = 0.415754209 Reorder the terms: -0.21875 + t = 0.415754209 Solving -0.21875 + t = 0.415754209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + t = 0.415754209 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + t = 0.415754209 + 0.21875 t = 0.415754209 + 0.21875 Combine like terms: 0.415754209 + 0.21875 = 0.634504209 t = 0.634504209 Simplifying t = 0.634504209Subproblem 2
t + -0.21875 = -0.415754209 Simplifying t + -0.21875 = -0.415754209 Reorder the terms: -0.21875 + t = -0.415754209 Solving -0.21875 + t = -0.415754209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + t = -0.415754209 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + t = -0.415754209 + 0.21875 t = -0.415754209 + 0.21875 Combine like terms: -0.415754209 + 0.21875 = -0.197004209 t = -0.197004209 Simplifying t = -0.197004209Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.634504209, -0.197004209}Solution
t = {0, 0.634504209, -0.197004209}
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