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Simplifying 8t + -16t2 + 3.5 = 0 Reorder the terms: 3.5 + 8t + -16t2 = 0 Solving 3.5 + 8t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.21875 + -0.5t + t2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + -0.5t + 0.21875 + t2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + -0.5t + t2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + -0.5t + t2 = 0 + 0.21875 -0.5t + t2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 -0.5t + t2 = 0.21875 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 = 0.21875 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 0.21875 + 0.0625 Combine like terms: 0.21875 + 0.0625 = 0.28125 0.0625 + -0.5t + t2 = 0.28125 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 0.28125 Calculate the square root of the right side: 0.530330086 Break this problem into two subproblems by setting (t + -0.25) equal to 0.530330086 and -0.530330086.Subproblem 1
t + -0.25 = 0.530330086 Simplifying t + -0.25 = 0.530330086 Reorder the terms: -0.25 + t = 0.530330086 Solving -0.25 + t = 0.530330086 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 = 0.530330086 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 0.530330086 + 0.25 t = 0.530330086 + 0.25 Combine like terms: 0.530330086 + 0.25 = 0.780330086 t = 0.780330086 Simplifying t = 0.780330086Subproblem 2
t + -0.25 = -0.530330086 Simplifying t + -0.25 = -0.530330086 Reorder the terms: -0.25 + t = -0.530330086 Solving -0.25 + t = -0.530330086 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 = -0.530330086 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -0.530330086 + 0.25 t = -0.530330086 + 0.25 Combine like terms: -0.530330086 + 0.25 = -0.280330086 t = -0.280330086 Simplifying t = -0.280330086Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.780330086, -0.280330086}
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