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Simplifying 0 = 16t2 + 62t + 4 Reorder the terms: 0 = 4 + 62t + 16t2 Solving 0 = 4 + 62t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -62t + -16t2 = 4 + 62t + 16t2 + -4 + -62t + -16t2 Reorder the terms: -4 + -62t + -16t2 = 4 + -4 + 62t + -62t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -62t + -16t2 = 0 + 62t + -62t + 16t2 + -16t2 -4 + -62t + -16t2 = 62t + -62t + 16t2 + -16t2 Combine like terms: 62t + -62t = 0 -4 + -62t + -16t2 = 0 + 16t2 + -16t2 -4 + -62t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -62t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 31t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 31t + 8t2)' equal to zero and attempt to solve: Simplifying 2 + 31t + 8t2 = 0 Solving 2 + 31t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + 3.875t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.875t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.875t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.875t + t2 = 0 + -0.25 3.875t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.875t + t2 = -0.25 The t term is 3.875t. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875t + 3.75390625 + t2 = -0.25 + 3.75390625 Reorder the terms: 3.75390625 + 3.875t + t2 = -0.25 + 3.75390625 Combine like terms: -0.25 + 3.75390625 = 3.50390625 3.75390625 + 3.875t + t2 = 3.50390625 Factor a perfect square on the left side: (t + 1.9375)(t + 1.9375) = 3.50390625 Calculate the square root of the right side: 1.871872391 Break this problem into two subproblems by setting (t + 1.9375) equal to 1.871872391 and -1.871872391.Subproblem 1
t + 1.9375 = 1.871872391 Simplifying t + 1.9375 = 1.871872391 Reorder the terms: 1.9375 + t = 1.871872391 Solving 1.9375 + t = 1.871872391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + t = 1.871872391 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + t = 1.871872391 + -1.9375 t = 1.871872391 + -1.9375 Combine like terms: 1.871872391 + -1.9375 = -0.065627609 t = -0.065627609 Simplifying t = -0.065627609Subproblem 2
t + 1.9375 = -1.871872391 Simplifying t + 1.9375 = -1.871872391 Reorder the terms: 1.9375 + t = -1.871872391 Solving 1.9375 + t = -1.871872391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + t = -1.871872391 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + t = -1.871872391 + -1.9375 t = -1.871872391 + -1.9375 Combine like terms: -1.871872391 + -1.9375 = -3.809372391 t = -3.809372391 Simplifying t = -3.809372391Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.065627609, -3.809372391}Solution
t = {-0.065627609, -3.809372391}
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