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Simplifying -16t2 + 64t + 40 = 0 Reorder the terms: 40 + 64t + -16t2 = 0 Solving 40 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(5 + 8t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + 8t + -2t2)' equal to zero and attempt to solve: Simplifying 5 + 8t + -2t2 = 0 Solving 5 + 8t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -4t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4t + t2 = 0 + 2.5 -4t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4t + t2 = 2.5 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 = 2.5 + 4 Reorder the terms: 4 + -4t + t2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 4 + -4t + t2 = 6.5 Factor a perfect square on the left side: (t + -2)(t + -2) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (t + -2) equal to 2.549509757 and -2.549509757.Subproblem 1
t + -2 = 2.549509757 Simplifying t + -2 = 2.549509757 Reorder the terms: -2 + t = 2.549509757 Solving -2 + t = 2.549509757 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 = 2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.549509757 + 2 t = 2.549509757 + 2 Combine like terms: 2.549509757 + 2 = 4.549509757 t = 4.549509757 Simplifying t = 4.549509757Subproblem 2
t + -2 = -2.549509757 Simplifying t + -2 = -2.549509757 Reorder the terms: -2 + t = -2.549509757 Solving -2 + t = -2.549509757 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 = -2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.549509757 + 2 t = -2.549509757 + 2 Combine like terms: -2.549509757 + 2 = -0.549509757 t = -0.549509757 Simplifying t = -0.549509757Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.549509757, -0.549509757}Solution
t = {4.549509757, -0.549509757}
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