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Simplifying 0 = -16t2 + -50t + 120 Reorder the terms: 0 = 120 + -50t + -16t2 Solving 0 = 120 + -50t + -16t2 Solving for variable 't'. Combine like terms: 0 + -120 = -120 -120 + 50t + 16t2 = 120 + -50t + -16t2 + -120 + 50t + 16t2 Reorder the terms: -120 + 50t + 16t2 = 120 + -120 + -50t + 50t + -16t2 + 16t2 Combine like terms: 120 + -120 = 0 -120 + 50t + 16t2 = 0 + -50t + 50t + -16t2 + 16t2 -120 + 50t + 16t2 = -50t + 50t + -16t2 + 16t2 Combine like terms: -50t + 50t = 0 -120 + 50t + 16t2 = 0 + -16t2 + 16t2 -120 + 50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -120 + 50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 25t + 8t2)' equal to zero and attempt to solve: Simplifying -60 + 25t + 8t2 = 0 Solving -60 + 25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.5 + 3.125t + t2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 3.125t + 7.5 + t2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 3.125t + t2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 3.125t + t2 = 0 + 7.5 3.125t + t2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 3.125t + t2 = 7.5 The t term is 3.125t. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125t + 2.44140625 + t2 = 7.5 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = 7.5 + 2.44140625 Combine like terms: 7.5 + 2.44140625 = 9.94140625 2.44140625 + 3.125t + t2 = 9.94140625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 9.94140625 Calculate the square root of the right side: 3.152999564 Break this problem into two subproblems by setting (t + 1.5625) equal to 3.152999564 and -3.152999564.Subproblem 1
t + 1.5625 = 3.152999564 Simplifying t + 1.5625 = 3.152999564 Reorder the terms: 1.5625 + t = 3.152999564 Solving 1.5625 + t = 3.152999564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = 3.152999564 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 3.152999564 + -1.5625 t = 3.152999564 + -1.5625 Combine like terms: 3.152999564 + -1.5625 = 1.590499564 t = 1.590499564 Simplifying t = 1.590499564Subproblem 2
t + 1.5625 = -3.152999564 Simplifying t + 1.5625 = -3.152999564 Reorder the terms: 1.5625 + t = -3.152999564 Solving 1.5625 + t = -3.152999564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = -3.152999564 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -3.152999564 + -1.5625 t = -3.152999564 + -1.5625 Combine like terms: -3.152999564 + -1.5625 = -4.715499564 t = -4.715499564 Simplifying t = -4.715499564Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.590499564, -4.715499564}Solution
t = {1.590499564, -4.715499564}
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