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Simplifying 0 = -16t2 + 50t + 160 Reorder the terms: 0 = 160 + 50t + -16t2 Solving 0 = 160 + 50t + -16t2 Solving for variable 't'. Combine like terms: 0 + -160 = -160 -160 + -50t + 16t2 = 160 + 50t + -16t2 + -160 + -50t + 16t2 Reorder the terms: -160 + -50t + 16t2 = 160 + -160 + 50t + -50t + -16t2 + 16t2 Combine like terms: 160 + -160 = 0 -160 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 -160 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -160 + -50t + 16t2 = 0 + -16t2 + 16t2 -160 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -160 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying -80 + -25t + 8t2 = 0 Solving -80 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10 + -3.125t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -3.125t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -3.125t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3.125t + t2 = 0 + 10 -3.125t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3.125t + t2 = 10 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 = 10 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 10 + 2.44140625 Combine like terms: 10 + 2.44140625 = 12.44140625 2.44140625 + -3.125t + t2 = 12.44140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 12.44140625 Calculate the square root of the right side: 3.527237765 Break this problem into two subproblems by setting (t + -1.5625) equal to 3.527237765 and -3.527237765.Subproblem 1
t + -1.5625 = 3.527237765 Simplifying t + -1.5625 = 3.527237765 Reorder the terms: -1.5625 + t = 3.527237765 Solving -1.5625 + t = 3.527237765 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 = 3.527237765 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 3.527237765 + 1.5625 t = 3.527237765 + 1.5625 Combine like terms: 3.527237765 + 1.5625 = 5.089737765 t = 5.089737765 Simplifying t = 5.089737765Subproblem 2
t + -1.5625 = -3.527237765 Simplifying t + -1.5625 = -3.527237765 Reorder the terms: -1.5625 + t = -3.527237765 Solving -1.5625 + t = -3.527237765 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 = -3.527237765 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -3.527237765 + 1.5625 t = -3.527237765 + 1.5625 Combine like terms: -3.527237765 + 1.5625 = -1.964737765 t = -1.964737765 Simplifying t = -1.964737765Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.089737765, -1.964737765}Solution
t = {5.089737765, -1.964737765}
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