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Simplifying 16t2 + -64t + -44 = 0 Reorder the terms: -44 + -64t + 16t2 = 0 Solving -44 + -64t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + -16t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + -16t + 4t2)' equal to zero and attempt to solve: Simplifying -11 + -16t + 4t2 = 0 Solving -11 + -16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -4t + t2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -4t + 2.75 + t2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -4t + t2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -4t + t2 = 0 + 2.75 -4t + t2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -4t + t2 = 2.75 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 2.75 + 4 Reorder the terms: 4 + -4t + t2 = 2.75 + 4 Combine like terms: 2.75 + 4 = 6.75 4 + -4t + t2 = 6.75 Factor a perfect square on the left side: (t + -2)(t + -2) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (t + -2) equal to 2.598076211 and -2.598076211.Subproblem 1
t + -2 = 2.598076211 Simplifying t + -2 = 2.598076211 Reorder the terms: -2 + t = 2.598076211 Solving -2 + t = 2.598076211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.598076211 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.598076211 + 2 t = 2.598076211 + 2 Combine like terms: 2.598076211 + 2 = 4.598076211 t = 4.598076211 Simplifying t = 4.598076211Subproblem 2
t + -2 = -2.598076211 Simplifying t + -2 = -2.598076211 Reorder the terms: -2 + t = -2.598076211 Solving -2 + t = -2.598076211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.598076211 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.598076211 + 2 t = -2.598076211 + 2 Combine like terms: -2.598076211 + 2 = -0.598076211 t = -0.598076211 Simplifying t = -0.598076211Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.598076211, -0.598076211}Solution
t = {4.598076211, -0.598076211}
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