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Simplifying -16t2 + 50t + 20 = 0 Reorder the terms: 20 + 50t + -16t2 = 0 Solving 20 + 50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 25t + -8t2)' equal to zero and attempt to solve: Simplifying 10 + 25t + -8t2 = 0 Solving 10 + 25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.25 + -3.125t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3.125t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3.125t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3.125t + t2 = 0 + 1.25 -3.125t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3.125t + t2 = 1.25 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 = 1.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 1.25 + 2.44140625 Combine like terms: 1.25 + 2.44140625 = 3.69140625 2.44140625 + -3.125t + t2 = 3.69140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 3.69140625 Calculate the square root of the right side: 1.921303269 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.921303269 and -1.921303269.Subproblem 1
t + -1.5625 = 1.921303269 Simplifying t + -1.5625 = 1.921303269 Reorder the terms: -1.5625 + t = 1.921303269 Solving -1.5625 + t = 1.921303269 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 = 1.921303269 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.921303269 + 1.5625 t = 1.921303269 + 1.5625 Combine like terms: 1.921303269 + 1.5625 = 3.483803269 t = 3.483803269 Simplifying t = 3.483803269Subproblem 2
t + -1.5625 = -1.921303269 Simplifying t + -1.5625 = -1.921303269 Reorder the terms: -1.5625 + t = -1.921303269 Solving -1.5625 + t = -1.921303269 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 = -1.921303269 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.921303269 + 1.5625 t = -1.921303269 + 1.5625 Combine like terms: -1.921303269 + 1.5625 = -0.358803269 t = -0.358803269 Simplifying t = -0.358803269Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.483803269, -0.358803269}Solution
t = {3.483803269, -0.358803269}
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