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Simplifying 4 + 23t + -16t2 = 0 Solving 4 + 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'. -0.25 + -1.4375t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.4375t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.4375t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.4375t + t2 = 0 + 0.25 -1.4375t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.4375t + t2 = 0.25 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 = 0.25 + 0.5166015625 Reorder the terms: 0.5166015625 + -1.4375t + t2 = 0.25 + 0.5166015625 Combine like terms: 0.25 + 0.5166015625 = 0.7666015625 0.5166015625 + -1.4375t + t2 = 0.7666015625 Factor a perfect square on the left side: (t + -0.71875)(t + -0.71875) = 0.7666015625 Calculate the square root of the right side: 0.875557858 Break this problem into two subproblems by setting (t + -0.71875) equal to 0.875557858 and -0.875557858.Subproblem 1
t + -0.71875 = 0.875557858 Simplifying t + -0.71875 = 0.875557858 Reorder the terms: -0.71875 + t = 0.875557858 Solving -0.71875 + t = 0.875557858 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 = 0.875557858 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + t = 0.875557858 + 0.71875 t = 0.875557858 + 0.71875 Combine like terms: 0.875557858 + 0.71875 = 1.594307858 t = 1.594307858 Simplifying t = 1.594307858Subproblem 2
t + -0.71875 = -0.875557858 Simplifying t + -0.71875 = -0.875557858 Reorder the terms: -0.71875 + t = -0.875557858 Solving -0.71875 + t = -0.875557858 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 = -0.875557858 + 0.71875 Combine like terms: -0.71875 + 0.71875 = 0.00000 0.00000 + t = -0.875557858 + 0.71875 t = -0.875557858 + 0.71875 Combine like terms: -0.875557858 + 0.71875 = -0.156807858 t = -0.156807858 Simplifying t = -0.156807858Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.594307858, -0.156807858}
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