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Simplifying 1025 + 5t + -16t2 = 0 Solving 1025 + 5t + -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'. -64.0625 + -0.3125t + t2 = 0 Move the constant term to the right: Add '64.0625' to each side of the equation. -64.0625 + -0.3125t + 64.0625 + t2 = 0 + 64.0625 Reorder the terms: -64.0625 + 64.0625 + -0.3125t + t2 = 0 + 64.0625 Combine like terms: -64.0625 + 64.0625 = 0.0000 0.0000 + -0.3125t + t2 = 0 + 64.0625 -0.3125t + t2 = 0 + 64.0625 Combine like terms: 0 + 64.0625 = 64.0625 -0.3125t + t2 = 64.0625 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 64.0625 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 64.0625 + 0.0244140625 Combine like terms: 64.0625 + 0.0244140625 = 64.0869140625 0.0244140625 + -0.3125t + t2 = 64.0869140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 64.0869140625 Calculate the square root of the right side: 8.005430286 Break this problem into two subproblems by setting (t + -0.15625) equal to 8.005430286 and -8.005430286.Subproblem 1
t + -0.15625 = 8.005430286 Simplifying t + -0.15625 = 8.005430286 Reorder the terms: -0.15625 + t = 8.005430286 Solving -0.15625 + t = 8.005430286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 8.005430286 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 8.005430286 + 0.15625 t = 8.005430286 + 0.15625 Combine like terms: 8.005430286 + 0.15625 = 8.161680286 t = 8.161680286 Simplifying t = 8.161680286Subproblem 2
t + -0.15625 = -8.005430286 Simplifying t + -0.15625 = -8.005430286 Reorder the terms: -0.15625 + t = -8.005430286 Solving -0.15625 + t = -8.005430286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -8.005430286 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -8.005430286 + 0.15625 t = -8.005430286 + 0.15625 Combine like terms: -8.005430286 + 0.15625 = -7.849180286 t = -7.849180286 Simplifying t = -7.849180286Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.161680286, -7.849180286}
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