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Simplifying -16t2 + 56t + 25 = 0 Reorder the terms: 25 + 56t + -16t2 = 0 Solving 25 + 56t + -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'. -1.5625 + -3.5t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -3.5t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -3.5t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -3.5t + t2 = 0 + 1.5625 -3.5t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -3.5t + t2 = 1.5625 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 = 1.5625 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 1.5625 + 3.0625 Combine like terms: 1.5625 + 3.0625 = 4.625 3.0625 + -3.5t + t2 = 4.625 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 4.625 Calculate the square root of the right side: 2.150581317 Break this problem into two subproblems by setting (t + -1.75) equal to 2.150581317 and -2.150581317.Subproblem 1
t + -1.75 = 2.150581317 Simplifying t + -1.75 = 2.150581317 Reorder the terms: -1.75 + t = 2.150581317 Solving -1.75 + t = 2.150581317 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 = 2.150581317 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 2.150581317 + 1.75 t = 2.150581317 + 1.75 Combine like terms: 2.150581317 + 1.75 = 3.900581317 t = 3.900581317 Simplifying t = 3.900581317Subproblem 2
t + -1.75 = -2.150581317 Simplifying t + -1.75 = -2.150581317 Reorder the terms: -1.75 + t = -2.150581317 Solving -1.75 + t = -2.150581317 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 = -2.150581317 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -2.150581317 + 1.75 t = -2.150581317 + 1.75 Combine like terms: -2.150581317 + 1.75 = -0.400581317 t = -0.400581317 Simplifying t = -0.400581317Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.900581317, -0.400581317}
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