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Simplifying -16t2 + 96t + -64 = 0 Reorder the terms: -64 + 96t + -16t2 = 0 Solving -64 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-4 + 6t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-4 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying -4 + 6t + -1t2 = 0 Solving -4 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -6t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -6t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6t + t2 = 0 + -4 -6t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6t + t2 = -4 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -4 + 9 Reorder the terms: 9 + -6t + t2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6t + t2 = 5 Factor a perfect square on the left side: (t + -3)(t + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
t + -3 = 2.236067978 Simplifying t + -3 = 2.236067978 Reorder the terms: -3 + t = 2.236067978 Solving -3 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.236067978 + 3 t = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 t = 5.236067978 Simplifying t = 5.236067978Subproblem 2
t + -3 = -2.236067978 Simplifying t + -3 = -2.236067978 Reorder the terms: -3 + t = -2.236067978 Solving -3 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.236067978 + 3 t = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 t = 0.763932022 Simplifying t = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.236067978, 0.763932022}Solution
t = {5.236067978, 0.763932022}
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