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Simplifying -16t2 + -40t + 280 = 0 Reorder the terms: 280 + -40t + -16t2 = 0 Solving 280 + -40t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(35 + -5t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(35 + -5t + -2t2)' equal to zero and attempt to solve: Simplifying 35 + -5t + -2t2 = 0 Solving 35 + -5t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -17.5 + 2.5t + t2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 2.5t + 17.5 + t2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 2.5t + t2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 2.5t + t2 = 0 + 17.5 2.5t + t2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 2.5t + t2 = 17.5 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 17.5 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 17.5 + 1.5625 Combine like terms: 17.5 + 1.5625 = 19.0625 1.5625 + 2.5t + t2 = 19.0625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (t + 1.25) equal to 4.366062299 and -4.366062299.Subproblem 1
t + 1.25 = 4.366062299 Simplifying t + 1.25 = 4.366062299 Reorder the terms: 1.25 + t = 4.366062299 Solving 1.25 + t = 4.366062299 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 4.366062299 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 4.366062299 + -1.25 t = 4.366062299 + -1.25 Combine like terms: 4.366062299 + -1.25 = 3.116062299 t = 3.116062299 Simplifying t = 3.116062299Subproblem 2
t + 1.25 = -4.366062299 Simplifying t + 1.25 = -4.366062299 Reorder the terms: 1.25 + t = -4.366062299 Solving 1.25 + t = -4.366062299 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -4.366062299 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -4.366062299 + -1.25 t = -4.366062299 + -1.25 Combine like terms: -4.366062299 + -1.25 = -5.616062299 t = -5.616062299 Simplifying t = -5.616062299Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.116062299, -5.616062299}Solution
t = {3.116062299, -5.616062299}
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