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Simplifying 16t2 + -128t + 64 = 0 Reorder the terms: 64 + -128t + 16t2 = 0 Solving 64 + -128t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(4 + -8t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(4 + -8t + t2)' equal to zero and attempt to solve: Simplifying 4 + -8t + t2 = 0 Solving 4 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -8t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8t + t2 = 0 + -4 -8t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8t + t2 = -4 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 = -4 + 16 Reorder the terms: 16 + -8t + t2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8t + t2 = 12 Factor a perfect square on the left side: (t + -4)(t + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
t + -4 = 3.464101615 Simplifying t + -4 = 3.464101615 Reorder the terms: -4 + t = 3.464101615 Solving -4 + t = 3.464101615 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 = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.464101615 + 4 t = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 t = 7.464101615 Simplifying t = 7.464101615Subproblem 2
t + -4 = -3.464101615 Simplifying t + -4 = -3.464101615 Reorder the terms: -4 + t = -3.464101615 Solving -4 + t = -3.464101615 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 = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.464101615 + 4 t = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 t = 0.535898385 Simplifying t = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.464101615, 0.535898385}Solution
t = {7.464101615, 0.535898385}
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