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Simplifying -16t2 + 16t + 775 = 0 Reorder the terms: 775 + 16t + -16t2 = 0 Solving 775 + 16t + -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'. -48.4375 + -1t + t2 = 0 Move the constant term to the right: Add '48.4375' to each side of the equation. -48.4375 + -1t + 48.4375 + t2 = 0 + 48.4375 Reorder the terms: -48.4375 + 48.4375 + -1t + t2 = 0 + 48.4375 Combine like terms: -48.4375 + 48.4375 = 0.0000 0.0000 + -1t + t2 = 0 + 48.4375 -1t + t2 = 0 + 48.4375 Combine like terms: 0 + 48.4375 = 48.4375 -1t + t2 = 48.4375 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 48.4375 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 48.4375 + 0.25 Combine like terms: 48.4375 + 0.25 = 48.6875 0.25 + -1t + t2 = 48.6875 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 48.6875 Calculate the square root of the right side: 6.977642868 Break this problem into two subproblems by setting (t + -0.5) equal to 6.977642868 and -6.977642868.Subproblem 1
t + -0.5 = 6.977642868 Simplifying t + -0.5 = 6.977642868 Reorder the terms: -0.5 + t = 6.977642868 Solving -0.5 + t = 6.977642868 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 6.977642868 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 6.977642868 + 0.5 t = 6.977642868 + 0.5 Combine like terms: 6.977642868 + 0.5 = 7.477642868 t = 7.477642868 Simplifying t = 7.477642868Subproblem 2
t + -0.5 = -6.977642868 Simplifying t + -0.5 = -6.977642868 Reorder the terms: -0.5 + t = -6.977642868 Solving -0.5 + t = -6.977642868 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -6.977642868 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -6.977642868 + 0.5 t = -6.977642868 + 0.5 Combine like terms: -6.977642868 + 0.5 = -6.477642868 t = -6.477642868 Simplifying t = -6.477642868Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.477642868, -6.477642868}
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