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Simplifying 0 = 1 + 16t + -4t2 Solving 0 = 1 + 16t + -4t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -16t + 4t2 = 1 + 16t + -4t2 + -1 + -16t + 4t2 Reorder the terms: -1 + -16t + 4t2 = 1 + -1 + 16t + -16t + -4t2 + 4t2 Combine like terms: 1 + -1 = 0 -1 + -16t + 4t2 = 0 + 16t + -16t + -4t2 + 4t2 -1 + -16t + 4t2 = 16t + -16t + -4t2 + 4t2 Combine like terms: 16t + -16t = 0 -1 + -16t + 4t2 = 0 + -4t2 + 4t2 -1 + -16t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -1 + -16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -4t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4t + t2 = 0 + 0.25 -4t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4t + t2 = 0.25 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 0.25 + 4 Reorder the terms: 4 + -4t + t2 = 0.25 + 4 Combine like terms: 0.25 + 4 = 4.25 4 + -4t + t2 = 4.25 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (t + -2) equal to 2.061552813 and -2.061552813.Subproblem 1
t + -2 = 2.061552813 Simplifying t + -2 = 2.061552813 Reorder the terms: -2 + t = 2.061552813 Solving -2 + t = 2.061552813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.061552813 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.061552813 + 2 t = 2.061552813 + 2 Combine like terms: 2.061552813 + 2 = 4.061552813 t = 4.061552813 Simplifying t = 4.061552813Subproblem 2
t + -2 = -2.061552813 Simplifying t + -2 = -2.061552813 Reorder the terms: -2 + t = -2.061552813 Solving -2 + t = -2.061552813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.061552813 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.061552813 + 2 t = -2.061552813 + 2 Combine like terms: -2.061552813 + 2 = -0.061552813 t = -0.061552813 Simplifying t = -0.061552813Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.061552813, -0.061552813}
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