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Simplifying -16t2 + -23t + 200 = 0 Reorder the terms: 200 + -23t + -16t2 = 0 Solving 200 + -23t + -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'. -12.5 + 1.4375t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.4375t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.4375t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.4375t + t2 = 0 + 12.5 1.4375t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.4375t + t2 = 12.5 The t term is 1.4375t. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375t + 0.5166015625 + t2 = 12.5 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375t + t2 = 12.5 + 0.5166015625 Combine like terms: 12.5 + 0.5166015625 = 13.0166015625 0.5166015625 + 1.4375t + t2 = 13.0166015625 Factor a perfect square on the left side: (t + 0.71875)(t + 0.71875) = 13.0166015625 Calculate the square root of the right side: 3.607852763 Break this problem into two subproblems by setting (t + 0.71875) equal to 3.607852763 and -3.607852763.Subproblem 1
t + 0.71875 = 3.607852763 Simplifying t + 0.71875 = 3.607852763 Reorder the terms: 0.71875 + t = 3.607852763 Solving 0.71875 + t = 3.607852763 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + t = 3.607852763 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + t = 3.607852763 + -0.71875 t = 3.607852763 + -0.71875 Combine like terms: 3.607852763 + -0.71875 = 2.889102763 t = 2.889102763 Simplifying t = 2.889102763Subproblem 2
t + 0.71875 = -3.607852763 Simplifying t + 0.71875 = -3.607852763 Reorder the terms: 0.71875 + t = -3.607852763 Solving 0.71875 + t = -3.607852763 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + t = -3.607852763 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + t = -3.607852763 + -0.71875 t = -3.607852763 + -0.71875 Combine like terms: -3.607852763 + -0.71875 = -4.326602763 t = -4.326602763 Simplifying t = -4.326602763Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.889102763, -4.326602763}
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