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Simplifying 0 = -16t2 + 28t + 6 Reorder the terms: 0 = 6 + 28t + -16t2 Solving 0 = 6 + 28t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -28t + 16t2 = 6 + 28t + -16t2 + -6 + -28t + 16t2 Reorder the terms: -6 + -28t + 16t2 = 6 + -6 + 28t + -28t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -28t + 16t2 = 0 + 28t + -28t + -16t2 + 16t2 -6 + -28t + 16t2 = 28t + -28t + -16t2 + 16t2 Combine like terms: 28t + -28t = 0 -6 + -28t + 16t2 = 0 + -16t2 + 16t2 -6 + -28t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -28t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -14t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -14t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -14t + 8t2 = 0 Solving -3 + -14t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -1.75t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.75t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.75t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.75t + t2 = 0 + 0.375 -1.75t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.75t + t2 = 0.375 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = 0.375 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = 0.375 + 0.765625 Combine like terms: 0.375 + 0.765625 = 1.140625 0.765625 + -1.75t + t2 = 1.140625 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (t + -0.875) equal to 1.068000468 and -1.068000468.Subproblem 1
t + -0.875 = 1.068000468 Simplifying t + -0.875 = 1.068000468 Reorder the terms: -0.875 + t = 1.068000468 Solving -0.875 + t = 1.068000468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = 1.068000468 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 1.068000468 + 0.875 t = 1.068000468 + 0.875 Combine like terms: 1.068000468 + 0.875 = 1.943000468 t = 1.943000468 Simplifying t = 1.943000468Subproblem 2
t + -0.875 = -1.068000468 Simplifying t + -0.875 = -1.068000468 Reorder the terms: -0.875 + t = -1.068000468 Solving -0.875 + t = -1.068000468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = -1.068000468 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -1.068000468 + 0.875 t = -1.068000468 + 0.875 Combine like terms: -1.068000468 + 0.875 = -0.193000468 t = -0.193000468 Simplifying t = -0.193000468Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.943000468, -0.193000468}Solution
t = {1.943000468, -0.193000468}
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