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Simplifying 0 = 4 + 6t + -16t2 Solving 0 = 4 + 6t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -6t + 16t2 = 4 + 6t + -16t2 + -4 + -6t + 16t2 Reorder the terms: -4 + -6t + 16t2 = 4 + -4 + 6t + -6t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -6t + 16t2 = 0 + 6t + -6t + -16t2 + 16t2 -4 + -6t + 16t2 = 6t + -6t + -16t2 + 16t2 Combine like terms: 6t + -6t = 0 -4 + -6t + 16t2 = 0 + -16t2 + 16t2 -4 + -6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -3t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -3t + 8t2)' equal to zero and attempt to solve: Simplifying -2 + -3t + 8t2 = 0 Solving -2 + -3t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -0.375t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.375t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.375t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.375t + t2 = 0 + 0.25 -0.375t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.375t + t2 = 0.25 The t term is -0.375t. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375t + 0.03515625 + t2 = 0.25 + 0.03515625 Reorder the terms: 0.03515625 + -0.375t + t2 = 0.25 + 0.03515625 Combine like terms: 0.25 + 0.03515625 = 0.28515625 0.03515625 + -0.375t + t2 = 0.28515625 Factor a perfect square on the left side: (t + -0.1875)(t + -0.1875) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (t + -0.1875) equal to 0.534000234 and -0.534000234.Subproblem 1
t + -0.1875 = 0.534000234 Simplifying t + -0.1875 = 0.534000234 Reorder the terms: -0.1875 + t = 0.534000234 Solving -0.1875 + t = 0.534000234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + t = 0.534000234 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t = 0.534000234 + 0.1875 t = 0.534000234 + 0.1875 Combine like terms: 0.534000234 + 0.1875 = 0.721500234 t = 0.721500234 Simplifying t = 0.721500234Subproblem 2
t + -0.1875 = -0.534000234 Simplifying t + -0.1875 = -0.534000234 Reorder the terms: -0.1875 + t = -0.534000234 Solving -0.1875 + t = -0.534000234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + t = -0.534000234 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t = -0.534000234 + 0.1875 t = -0.534000234 + 0.1875 Combine like terms: -0.534000234 + 0.1875 = -0.346500234 t = -0.346500234 Simplifying t = -0.346500234Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.721500234, -0.346500234}Solution
t = {0.721500234, -0.346500234}
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