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Simplifying -16t2 + 4624 = t Reorder the terms: 4624 + -16t2 = t Solving 4624 + -16t2 = t Solving for variable 't'. Reorder the terms: 4624 + -1t + -16t2 = t + -1t Combine like terms: t + -1t = 0 4624 + -1t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -289 + 0.0625t + t2 = 0 Move the constant term to the right: Add '289' to each side of the equation. -289 + 0.0625t + 289 + t2 = 0 + 289 Reorder the terms: -289 + 289 + 0.0625t + t2 = 0 + 289 Combine like terms: -289 + 289 = 0 0 + 0.0625t + t2 = 0 + 289 0.0625t + t2 = 0 + 289 Combine like terms: 0 + 289 = 289 0.0625t + t2 = 289 The t term is 0.0625t. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625t + 0.0009765625 + t2 = 289 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625t + t2 = 289 + 0.0009765625 Combine like terms: 289 + 0.0009765625 = 289.0009765625 0.0009765625 + 0.0625t + t2 = 289.0009765625 Factor a perfect square on the left side: (t + 0.03125)(t + 0.03125) = 289.0009765625 Calculate the square root of the right side: 17.000028722 Break this problem into two subproblems by setting (t + 0.03125) equal to 17.000028722 and -17.000028722.Subproblem 1
t + 0.03125 = 17.000028722 Simplifying t + 0.03125 = 17.000028722 Reorder the terms: 0.03125 + t = 17.000028722 Solving 0.03125 + t = 17.000028722 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = 17.000028722 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = 17.000028722 + -0.03125 t = 17.000028722 + -0.03125 Combine like terms: 17.000028722 + -0.03125 = 16.968778722 t = 16.968778722 Simplifying t = 16.968778722Subproblem 2
t + 0.03125 = -17.000028722 Simplifying t + 0.03125 = -17.000028722 Reorder the terms: 0.03125 + t = -17.000028722 Solving 0.03125 + t = -17.000028722 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + t = -17.000028722 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + t = -17.000028722 + -0.03125 t = -17.000028722 + -0.03125 Combine like terms: -17.000028722 + -0.03125 = -17.031278722 t = -17.031278722 Simplifying t = -17.031278722Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.968778722, -17.031278722}
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