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Simplifying 0 = -16t2 + 70t + 4 Reorder the terms: 0 = 4 + 70t + -16t2 Solving 0 = 4 + 70t + -16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -70t + 16t2 = 4 + 70t + -16t2 + -4 + -70t + 16t2 Reorder the terms: -4 + -70t + 16t2 = 4 + -4 + 70t + -70t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -70t + 16t2 = 0 + 70t + -70t + -16t2 + 16t2 -4 + -70t + 16t2 = 70t + -70t + -16t2 + 16t2 Combine like terms: 70t + -70t = 0 -4 + -70t + 16t2 = 0 + -16t2 + 16t2 -4 + -70t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -70t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -35t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -35t + 8t2)' equal to zero and attempt to solve: Simplifying -2 + -35t + 8t2 = 0 Solving -2 + -35t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -4.375t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4.375t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4.375t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4.375t + t2 = 0 + 0.25 -4.375t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4.375t + t2 = 0.25 The t term is -4.375t. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375t + 4.78515625 + t2 = 0.25 + 4.78515625 Reorder the terms: 4.78515625 + -4.375t + t2 = 0.25 + 4.78515625 Combine like terms: 0.25 + 4.78515625 = 5.03515625 4.78515625 + -4.375t + t2 = 5.03515625 Factor a perfect square on the left side: (t + -2.1875)(t + -2.1875) = 5.03515625 Calculate the square root of the right side: 2.243915384 Break this problem into two subproblems by setting (t + -2.1875) equal to 2.243915384 and -2.243915384.Subproblem 1
t + -2.1875 = 2.243915384 Simplifying t + -2.1875 = 2.243915384 Reorder the terms: -2.1875 + t = 2.243915384 Solving -2.1875 + t = 2.243915384 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = 2.243915384 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = 2.243915384 + 2.1875 t = 2.243915384 + 2.1875 Combine like terms: 2.243915384 + 2.1875 = 4.431415384 t = 4.431415384 Simplifying t = 4.431415384Subproblem 2
t + -2.1875 = -2.243915384 Simplifying t + -2.1875 = -2.243915384 Reorder the terms: -2.1875 + t = -2.243915384 Solving -2.1875 + t = -2.243915384 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = -2.243915384 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = -2.243915384 + 2.1875 t = -2.243915384 + 2.1875 Combine like terms: -2.243915384 + 2.1875 = -0.056415384 t = -0.056415384 Simplifying t = -0.056415384Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.431415384, -0.056415384}Solution
t = {4.431415384, -0.056415384}
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