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Simplifying -16t2 + 63t + 16 = 0 Reorder the terms: 16 + 63t + -16t2 = 0 Solving 16 + 63t + -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'. -1 + -3.9375t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.9375t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -3.9375t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.9375t + t2 = 0 + 1 -3.9375t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.9375t + t2 = 1 The t term is -3.9375t. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375t + 3.875976563 + t2 = 1 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375t + t2 = 1 + 3.875976563 Combine like terms: 1 + 3.875976563 = 4.875976563 3.875976563 + -3.9375t + t2 = 4.875976563 Factor a perfect square on the left side: (t + -1.96875)(t + -1.96875) = 4.875976563 Calculate the square root of the right side: 2.208161353 Break this problem into two subproblems by setting (t + -1.96875) equal to 2.208161353 and -2.208161353.Subproblem 1
t + -1.96875 = 2.208161353 Simplifying t + -1.96875 = 2.208161353 Reorder the terms: -1.96875 + t = 2.208161353 Solving -1.96875 + t = 2.208161353 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + t = 2.208161353 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + t = 2.208161353 + 1.96875 t = 2.208161353 + 1.96875 Combine like terms: 2.208161353 + 1.96875 = 4.176911353 t = 4.176911353 Simplifying t = 4.176911353Subproblem 2
t + -1.96875 = -2.208161353 Simplifying t + -1.96875 = -2.208161353 Reorder the terms: -1.96875 + t = -2.208161353 Solving -1.96875 + t = -2.208161353 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + t = -2.208161353 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + t = -2.208161353 + 1.96875 t = -2.208161353 + 1.96875 Combine like terms: -2.208161353 + 1.96875 = -0.239411353 t = -0.239411353 Simplifying t = -0.239411353Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.176911353, -0.239411353}
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