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Simplifying -16t2 + 128t + 26 = 0 Reorder the terms: 26 + 128t + -16t2 = 0 Solving 26 + 128t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + 64t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + 64t + -8t2)' equal to zero and attempt to solve: Simplifying 13 + 64t + -8t2 = 0 Solving 13 + 64t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.625 + -8t + t2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -8t + 1.625 + t2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -8t + t2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -8t + t2 = 0 + 1.625 -8t + t2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -8t + t2 = 1.625 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 1.625 + 16 Reorder the terms: 16 + -8t + t2 = 1.625 + 16 Combine like terms: 1.625 + 16 = 17.625 16 + -8t + t2 = 17.625 Factor a perfect square on the left side: (t + -4)(t + -4) = 17.625 Calculate the square root of the right side: 4.198213906 Break this problem into two subproblems by setting (t + -4) equal to 4.198213906 and -4.198213906.Subproblem 1
t + -4 = 4.198213906 Simplifying t + -4 = 4.198213906 Reorder the terms: -4 + t = 4.198213906 Solving -4 + t = 4.198213906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.198213906 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.198213906 + 4 t = 4.198213906 + 4 Combine like terms: 4.198213906 + 4 = 8.198213906 t = 8.198213906 Simplifying t = 8.198213906Subproblem 2
t + -4 = -4.198213906 Simplifying t + -4 = -4.198213906 Reorder the terms: -4 + t = -4.198213906 Solving -4 + t = -4.198213906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.198213906 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.198213906 + 4 t = -4.198213906 + 4 Combine like terms: -4.198213906 + 4 = -0.198213906 t = -0.198213906 Simplifying t = -0.198213906Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.198213906, -0.198213906}Solution
t = {8.198213906, -0.198213906}
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