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Simplifying -16t2 + -128t + 128 = 0 Reorder the terms: 128 + -128t + -16t2 = 0 Solving 128 + -128t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(8 + -8t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(8 + -8t + -1t2)' equal to zero and attempt to solve: Simplifying 8 + -8t + -1t2 = 0 Solving 8 + -8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 8t + t2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 8t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 8t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8t + t2 = 0 + 8 8t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 8t + t2 = 8 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 = 8 + 16 Reorder the terms: 16 + 8t + t2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + 8t + t2 = 24 Factor a perfect square on the left side: (t + 4)(t + 4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (t + 4) equal to 4.898979486 and -4.898979486.Subproblem 1
t + 4 = 4.898979486 Simplifying t + 4 = 4.898979486 Reorder the terms: 4 + t = 4.898979486 Solving 4 + t = 4.898979486 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 = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + t = 4.898979486 + -4 t = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 t = 0.898979486 Simplifying t = 0.898979486Subproblem 2
t + 4 = -4.898979486 Simplifying t + 4 = -4.898979486 Reorder the terms: 4 + t = -4.898979486 Solving 4 + t = -4.898979486 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 = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + t = -4.898979486 + -4 t = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 t = -8.898979486 Simplifying t = -8.898979486Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.898979486, -8.898979486}Solution
t = {0.898979486, -8.898979486}
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