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Simplifying 244 = 144t + -16t2 Solving 244 = 144t + -16t2 Solving for variable 't'. Reorder the terms: 244 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 244 + -144t + 16t2 = 0 + -16t2 + 16t2 244 + -144t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 244 + -144t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(61 + -36t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(61 + -36t + 4t2)' equal to zero and attempt to solve: Simplifying 61 + -36t + 4t2 = 0 Solving 61 + -36t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.25 + -9t + t2 = 0 Move the constant term to the right: Add '-15.25' to each side of the equation. 15.25 + -9t + -15.25 + t2 = 0 + -15.25 Reorder the terms: 15.25 + -15.25 + -9t + t2 = 0 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + -9t + t2 = 0 + -15.25 -9t + t2 = 0 + -15.25 Combine like terms: 0 + -15.25 = -15.25 -9t + t2 = -15.25 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -15.25 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -15.25 + 20.25 Combine like terms: -15.25 + 20.25 = 5 20.25 + -9t + t2 = 5 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t + -4.5) equal to 2.236067978 and -2.236067978.Subproblem 1
t + -4.5 = 2.236067978 Simplifying t + -4.5 = 2.236067978 Reorder the terms: -4.5 + t = 2.236067978 Solving -4.5 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 2.236067978 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 2.236067978 + 4.5 t = 2.236067978 + 4.5 Combine like terms: 2.236067978 + 4.5 = 6.736067978 t = 6.736067978 Simplifying t = 6.736067978Subproblem 2
t + -4.5 = -2.236067978 Simplifying t + -4.5 = -2.236067978 Reorder the terms: -4.5 + t = -2.236067978 Solving -4.5 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -2.236067978 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -2.236067978 + 4.5 t = -2.236067978 + 4.5 Combine like terms: -2.236067978 + 4.5 = 2.263932022 t = 2.263932022 Simplifying t = 2.263932022Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.736067978, 2.263932022}Solution
t = {6.736067978, 2.263932022}
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