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Simplifying -18 = -16t2 + -4t Reorder the terms: -18 = -4t + -16t2 Solving -18 = -4t + -16t2 Solving for variable 't'. Reorder the terms: -18 + 4t + 16t2 = -4t + 4t + -16t2 + 16t2 Combine like terms: -4t + 4t = 0 -18 + 4t + 16t2 = 0 + -16t2 + 16t2 -18 + 4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -18 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 2t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 2t + 8t2)' equal to zero and attempt to solve: Simplifying -9 + 2t + 8t2 = 0 Solving -9 + 2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 0.25t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.25t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.25t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.25t + t2 = 0 + 1.125 0.25t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.25t + t2 = 1.125 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = 1.125 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = 1.125 + 0.015625 Combine like terms: 1.125 + 0.015625 = 1.140625 0.015625 + 0.25t + t2 = 1.140625 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (t + 0.125) equal to 1.068000468 and -1.068000468.Subproblem 1
t + 0.125 = 1.068000468 Simplifying t + 0.125 = 1.068000468 Reorder the terms: 0.125 + t = 1.068000468 Solving 0.125 + t = 1.068000468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = 1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = 1.068000468 + -0.125 t = 1.068000468 + -0.125 Combine like terms: 1.068000468 + -0.125 = 0.943000468 t = 0.943000468 Simplifying t = 0.943000468Subproblem 2
t + 0.125 = -1.068000468 Simplifying t + 0.125 = -1.068000468 Reorder the terms: 0.125 + t = -1.068000468 Solving 0.125 + t = -1.068000468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = -1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = -1.068000468 + -0.125 t = -1.068000468 + -0.125 Combine like terms: -1.068000468 + -0.125 = -1.193000468 t = -1.193000468 Simplifying t = -1.193000468Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.943000468, -1.193000468}Solution
t = {0.943000468, -1.193000468}
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