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Simplifying -16t2 + 8t + 70 = 0 Reorder the terms: 70 + 8t + -16t2 = 0 Solving 70 + 8t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(35 + 4t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + 4t + -8t2)' equal to zero and attempt to solve: Simplifying 35 + 4t + -8t2 = 0 Solving 35 + 4t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.375 + -0.5t + t2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -0.5t + 4.375 + t2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -0.5t + t2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -0.5t + t2 = 0 + 4.375 -0.5t + t2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -0.5t + t2 = 4.375 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 = 4.375 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 4.375 + 0.0625 Combine like terms: 4.375 + 0.0625 = 4.4375 0.0625 + -0.5t + t2 = 4.4375 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 4.4375 Calculate the square root of the right side: 2.106537443 Break this problem into two subproblems by setting (t + -0.25) equal to 2.106537443 and -2.106537443.Subproblem 1
t + -0.25 = 2.106537443 Simplifying t + -0.25 = 2.106537443 Reorder the terms: -0.25 + t = 2.106537443 Solving -0.25 + t = 2.106537443 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 = 2.106537443 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 2.106537443 + 0.25 t = 2.106537443 + 0.25 Combine like terms: 2.106537443 + 0.25 = 2.356537443 t = 2.356537443 Simplifying t = 2.356537443Subproblem 2
t + -0.25 = -2.106537443 Simplifying t + -0.25 = -2.106537443 Reorder the terms: -0.25 + t = -2.106537443 Solving -0.25 + t = -2.106537443 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 = -2.106537443 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -2.106537443 + 0.25 t = -2.106537443 + 0.25 Combine like terms: -2.106537443 + 0.25 = -1.856537443 t = -1.856537443 Simplifying t = -1.856537443Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.356537443, -1.856537443}Solution
t = {2.356537443, -1.856537443}
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