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Simplifying -16t2 + 40t + 175 = 0 Reorder the terms: 175 + 40t + -16t2 = 0 Solving 175 + 40t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -10.9375 + -2.5t + t2 = 0 Move the constant term to the right: Add '10.9375' to each side of the equation. -10.9375 + -2.5t + 10.9375 + t2 = 0 + 10.9375 Reorder the terms: -10.9375 + 10.9375 + -2.5t + t2 = 0 + 10.9375 Combine like terms: -10.9375 + 10.9375 = 0.0000 0.0000 + -2.5t + t2 = 0 + 10.9375 -2.5t + t2 = 0 + 10.9375 Combine like terms: 0 + 10.9375 = 10.9375 -2.5t + t2 = 10.9375 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 = 10.9375 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 10.9375 + 1.5625 Combine like terms: 10.9375 + 1.5625 = 12.5 1.5625 + -2.5t + t2 = 12.5 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (t + -1.25) equal to 3.535533906 and -3.535533906.Subproblem 1
t + -1.25 = 3.535533906 Simplifying t + -1.25 = 3.535533906 Reorder the terms: -1.25 + t = 3.535533906 Solving -1.25 + t = 3.535533906 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 = 3.535533906 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 3.535533906 + 1.25 t = 3.535533906 + 1.25 Combine like terms: 3.535533906 + 1.25 = 4.785533906 t = 4.785533906 Simplifying t = 4.785533906Subproblem 2
t + -1.25 = -3.535533906 Simplifying t + -1.25 = -3.535533906 Reorder the terms: -1.25 + t = -3.535533906 Solving -1.25 + t = -3.535533906 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 = -3.535533906 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -3.535533906 + 1.25 t = -3.535533906 + 1.25 Combine like terms: -3.535533906 + 1.25 = -2.285533906 t = -2.285533906 Simplifying t = -2.285533906Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.785533906, -2.285533906}
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