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Simplifying 16t2 + -56t + -40 = 0 Reorder the terms: -40 + -56t + 16t2 = 0 Solving -40 + -56t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + -7t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -7t + 2t2)' equal to zero and attempt to solve: Simplifying -5 + -7t + 2t2 = 0 Solving -5 + -7t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3.5t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.5t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.5t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.5t + t2 = 0 + 2.5 -3.5t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.5t + t2 = 2.5 The t term is -3.5t. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5t + 3.0625 + t2 = 2.5 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 2.5 + 3.0625 Combine like terms: 2.5 + 3.0625 = 5.5625 3.0625 + -3.5t + t2 = 5.5625 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (t + -1.75) equal to 2.358495283 and -2.358495283.Subproblem 1
t + -1.75 = 2.358495283 Simplifying t + -1.75 = 2.358495283 Reorder the terms: -1.75 + t = 2.358495283 Solving -1.75 + t = 2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 2.358495283 + 1.75 t = 2.358495283 + 1.75 Combine like terms: 2.358495283 + 1.75 = 4.108495283 t = 4.108495283 Simplifying t = 4.108495283Subproblem 2
t + -1.75 = -2.358495283 Simplifying t + -1.75 = -2.358495283 Reorder the terms: -1.75 + t = -2.358495283 Solving -1.75 + t = -2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -2.358495283 + 1.75 t = -2.358495283 + 1.75 Combine like terms: -2.358495283 + 1.75 = -0.608495283 t = -0.608495283 Simplifying t = -0.608495283Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.108495283, -0.608495283}Solution
t = {4.108495283, -0.608495283}
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