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Simplifying 8(-2t2 + -1t + 8) = 0 Reorder the terms: 8(8 + -1t + -2t2) = 0 (8 * 8 + -1t * 8 + -2t2 * 8) = 0 (64 + -8t + -16t2) = 0 Solving 64 + -8t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(8 + -1t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(8 + -1t + -2t2)' equal to zero and attempt to solve: Simplifying 8 + -1t + -2t2 = 0 Solving 8 + -1t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4 + 0.5t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.5t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 0.5t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.5t + t2 = 0 + 4 0.5t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.5t + t2 = 4 The t term is 0.5t. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5t + 0.0625 + t2 = 4 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + 0.5t + t2 = 4.0625 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (t + 0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
t + 0.25 = 2.015564437 Simplifying t + 0.25 = 2.015564437 Reorder the terms: 0.25 + t = 2.015564437 Solving 0.25 + t = 2.015564437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = 2.015564437 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = 2.015564437 + -0.25 t = 2.015564437 + -0.25 Combine like terms: 2.015564437 + -0.25 = 1.765564437 t = 1.765564437 Simplifying t = 1.765564437Subproblem 2
t + 0.25 = -2.015564437 Simplifying t + 0.25 = -2.015564437 Reorder the terms: 0.25 + t = -2.015564437 Solving 0.25 + t = -2.015564437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = -2.015564437 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = -2.015564437 + -0.25 t = -2.015564437 + -0.25 Combine like terms: -2.015564437 + -0.25 = -2.265564437 t = -2.265564437 Simplifying t = -2.265564437Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.765564437, -2.265564437}Solution
t = {1.765564437, -2.265564437}
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