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Simplifying 16t2 + -50t + -10 = 0 Reorder the terms: -10 + -50t + 16t2 = 0 Solving -10 + -50t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying -5 + -25t + 8t2 = 0 Solving -5 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -3.125t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -3.125t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -3.125t + t2 = 0 + 0.625 -3.125t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -3.125t + t2 = 0.625 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 = 0.625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.625 + 2.44140625 Combine like terms: 0.625 + 2.44140625 = 3.06640625 2.44140625 + -3.125t + t2 = 3.06640625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 3.06640625 Calculate the square root of the right side: 1.751115716 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.751115716 and -1.751115716.Subproblem 1
t + -1.5625 = 1.751115716 Simplifying t + -1.5625 = 1.751115716 Reorder the terms: -1.5625 + t = 1.751115716 Solving -1.5625 + t = 1.751115716 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 = 1.751115716 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.751115716 + 1.5625 t = 1.751115716 + 1.5625 Combine like terms: 1.751115716 + 1.5625 = 3.313615716 t = 3.313615716 Simplifying t = 3.313615716Subproblem 2
t + -1.5625 = -1.751115716 Simplifying t + -1.5625 = -1.751115716 Reorder the terms: -1.5625 + t = -1.751115716 Solving -1.5625 + t = -1.751115716 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 = -1.751115716 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.751115716 + 1.5625 t = -1.751115716 + 1.5625 Combine like terms: -1.751115716 + 1.5625 = -0.188615716 t = -0.188615716 Simplifying t = -0.188615716Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.313615716, -0.188615716}Solution
t = {3.313615716, -0.188615716}
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