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Simplifying -16t2 + 220t + 5 = 0 Reorder the terms: 5 + 220t + -16t2 = 0 Solving 5 + 220t + -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'. -0.3125 + -13.75t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -13.75t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -13.75t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -13.75t + t2 = 0 + 0.3125 -13.75t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -13.75t + t2 = 0.3125 The t term is -13.75t. Take half its coefficient (-6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. -13.75t + 47.265625 + t2 = 0.3125 + 47.265625 Reorder the terms: 47.265625 + -13.75t + t2 = 0.3125 + 47.265625 Combine like terms: 0.3125 + 47.265625 = 47.578125 47.265625 + -13.75t + t2 = 47.578125 Factor a perfect square on the left side: (t + -6.875)(t + -6.875) = 47.578125 Calculate the square root of the right side: 6.897689831 Break this problem into two subproblems by setting (t + -6.875) equal to 6.897689831 and -6.897689831.Subproblem 1
t + -6.875 = 6.897689831 Simplifying t + -6.875 = 6.897689831 Reorder the terms: -6.875 + t = 6.897689831 Solving -6.875 + t = 6.897689831 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + t = 6.897689831 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + t = 6.897689831 + 6.875 t = 6.897689831 + 6.875 Combine like terms: 6.897689831 + 6.875 = 13.772689831 t = 13.772689831 Simplifying t = 13.772689831Subproblem 2
t + -6.875 = -6.897689831 Simplifying t + -6.875 = -6.897689831 Reorder the terms: -6.875 + t = -6.897689831 Solving -6.875 + t = -6.897689831 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + t = -6.897689831 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + t = -6.897689831 + 6.875 t = -6.897689831 + 6.875 Combine like terms: -6.897689831 + 6.875 = -0.022689831 t = -0.022689831 Simplifying t = -0.022689831Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.772689831, -0.022689831}
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