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Simplifying 40 = 16t2 + 88t Reorder the terms: 40 = 88t + 16t2 Solving 40 = 88t + 16t2 Solving for variable 't'. Reorder the terms: 40 + -88t + -16t2 = 88t + -88t + 16t2 + -16t2 Combine like terms: 88t + -88t = 0 40 + -88t + -16t2 = 0 + 16t2 + -16t2 40 + -88t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 40 + -88t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(5 + -11t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + -11t + -2t2)' equal to zero and attempt to solve: Simplifying 5 + -11t + -2t2 = 0 Solving 5 + -11t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + 5.5t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 5.5t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 5.5t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 5.5t + t2 = 0 + 2.5 5.5t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 5.5t + t2 = 2.5 The t term is 5.5t. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5t + 7.5625 + t2 = 2.5 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = 2.5 + 7.5625 Combine like terms: 2.5 + 7.5625 = 10.0625 7.5625 + 5.5t + t2 = 10.0625 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (t + 2.75) equal to 3.172144385 and -3.172144385.Subproblem 1
t + 2.75 = 3.172144385 Simplifying t + 2.75 = 3.172144385 Reorder the terms: 2.75 + t = 3.172144385 Solving 2.75 + t = 3.172144385 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = 3.172144385 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 3.172144385 + -2.75 t = 3.172144385 + -2.75 Combine like terms: 3.172144385 + -2.75 = 0.422144385 t = 0.422144385 Simplifying t = 0.422144385Subproblem 2
t + 2.75 = -3.172144385 Simplifying t + 2.75 = -3.172144385 Reorder the terms: 2.75 + t = -3.172144385 Solving 2.75 + t = -3.172144385 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = -3.172144385 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -3.172144385 + -2.75 t = -3.172144385 + -2.75 Combine like terms: -3.172144385 + -2.75 = -5.922144385 t = -5.922144385 Simplifying t = -5.922144385Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.422144385, -5.922144385}Solution
t = {0.422144385, -5.922144385}
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