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Simplifying -16t2 + 0.2t + 62 = 0 Reorder the terms: 62 + 0.2t + -16t2 = 0 Solving 62 + 0.2t + -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'. -3.875 + -0.0125t + t2 = 0 Move the constant term to the right: Add '3.875' to each side of the equation. -3.875 + -0.0125t + 3.875 + t2 = 0 + 3.875 Reorder the terms: -3.875 + 3.875 + -0.0125t + t2 = 0 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + -0.0125t + t2 = 0 + 3.875 -0.0125t + t2 = 0 + 3.875 Combine like terms: 0 + 3.875 = 3.875 -0.0125t + t2 = 3.875 The t term is -0.0125t. Take half its coefficient (-0.00625). Square it (0.0000390625) and add it to both sides. Add '0.0000390625' to each side of the equation. -0.0125t + 0.0000390625 + t2 = 3.875 + 0.0000390625 Reorder the terms: 0.0000390625 + -0.0125t + t2 = 3.875 + 0.0000390625 Combine like terms: 3.875 + 0.0000390625 = 3.8750390625 0.0000390625 + -0.0125t + t2 = 3.8750390625 Factor a perfect square on the left side: (t + -0.00625)(t + -0.00625) = 3.8750390625 Calculate the square root of the right side: 1.96851189 Break this problem into two subproblems by setting (t + -0.00625) equal to 1.96851189 and -1.96851189.Subproblem 1
t + -0.00625 = 1.96851189 Simplifying t + -0.00625 = 1.96851189 Reorder the terms: -0.00625 + t = 1.96851189 Solving -0.00625 + t = 1.96851189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.00625' to each side of the equation. -0.00625 + 0.00625 + t = 1.96851189 + 0.00625 Combine like terms: -0.00625 + 0.00625 = 0.00000 0.00000 + t = 1.96851189 + 0.00625 t = 1.96851189 + 0.00625 Combine like terms: 1.96851189 + 0.00625 = 1.97476189 t = 1.97476189 Simplifying t = 1.97476189Subproblem 2
t + -0.00625 = -1.96851189 Simplifying t + -0.00625 = -1.96851189 Reorder the terms: -0.00625 + t = -1.96851189 Solving -0.00625 + t = -1.96851189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.00625' to each side of the equation. -0.00625 + 0.00625 + t = -1.96851189 + 0.00625 Combine like terms: -0.00625 + 0.00625 = 0.00000 0.00000 + t = -1.96851189 + 0.00625 t = -1.96851189 + 0.00625 Combine like terms: -1.96851189 + 0.00625 = -1.96226189 t = -1.96226189 Simplifying t = -1.96226189Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.97476189, -1.96226189}
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