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Simplifying 0 = -8t2 + 5t + 25 Reorder the terms: 0 = 25 + 5t + -8t2 Solving 0 = 25 + 5t + -8t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + -5t + 8t2 = 25 + 5t + -8t2 + -25 + -5t + 8t2 Reorder the terms: -25 + -5t + 8t2 = 25 + -25 + 5t + -5t + -8t2 + 8t2 Combine like terms: 25 + -25 = 0 -25 + -5t + 8t2 = 0 + 5t + -5t + -8t2 + 8t2 -25 + -5t + 8t2 = 5t + -5t + -8t2 + 8t2 Combine like terms: 5t + -5t = 0 -25 + -5t + 8t2 = 0 + -8t2 + 8t2 -25 + -5t + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -25 + -5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + -0.625t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.625t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.625t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.625t + t2 = 0 + 3.125 -0.625t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.625t + t2 = 3.125 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = 3.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 3.125 + 0.09765625 Combine like terms: 3.125 + 0.09765625 = 3.22265625 0.09765625 + -0.625t + t2 = 3.22265625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 3.22265625 Calculate the square root of the right side: 1.795175827 Break this problem into two subproblems by setting (t + -0.3125) equal to 1.795175827 and -1.795175827.Subproblem 1
t + -0.3125 = 1.795175827 Simplifying t + -0.3125 = 1.795175827 Reorder the terms: -0.3125 + t = 1.795175827 Solving -0.3125 + t = 1.795175827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 1.795175827 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 1.795175827 + 0.3125 t = 1.795175827 + 0.3125 Combine like terms: 1.795175827 + 0.3125 = 2.107675827 t = 2.107675827 Simplifying t = 2.107675827Subproblem 2
t + -0.3125 = -1.795175827 Simplifying t + -0.3125 = -1.795175827 Reorder the terms: -0.3125 + t = -1.795175827 Solving -0.3125 + t = -1.795175827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -1.795175827 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -1.795175827 + 0.3125 t = -1.795175827 + 0.3125 Combine like terms: -1.795175827 + 0.3125 = -1.482675827 t = -1.482675827 Simplifying t = -1.482675827Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.107675827, -1.482675827}
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