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Simplifying 16t + -4.9t2 + 1.7 = 0 Reorder the terms: 1.7 + 16t + -4.9t2 = 0 Solving 1.7 + 16t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.3469387755 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '0.3469387755' to each side of the equation. -0.3469387755 + -3.265306122t + 0.3469387755 + t2 = 0 + 0.3469387755 Reorder the terms: -0.3469387755 + 0.3469387755 + -3.265306122t + t2 = 0 + 0.3469387755 Combine like terms: -0.3469387755 + 0.3469387755 = 0.0000000000 0.0000000000 + -3.265306122t + t2 = 0 + 0.3469387755 -3.265306122t + t2 = 0 + 0.3469387755 Combine like terms: 0 + 0.3469387755 = 0.3469387755 -3.265306122t + t2 = 0.3469387755 The t term is -3.265306122t. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122t + 2.665556018 + t2 = 0.3469387755 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = 0.3469387755 + 2.665556018 Combine like terms: 0.3469387755 + 2.665556018 = 3.0124947935 2.665556018 + -3.265306122t + t2 = 3.0124947935 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 3.0124947935 Calculate the square root of the right side: 1.735653996 Break this problem into two subproblems by setting (t + -1.632653061) equal to 1.735653996 and -1.735653996.Subproblem 1
t + -1.632653061 = 1.735653996 Simplifying t + -1.632653061 = 1.735653996 Reorder the terms: -1.632653061 + t = 1.735653996 Solving -1.632653061 + t = 1.735653996 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 1.735653996 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 1.735653996 + 1.632653061 t = 1.735653996 + 1.632653061 Combine like terms: 1.735653996 + 1.632653061 = 3.368307057 t = 3.368307057 Simplifying t = 3.368307057Subproblem 2
t + -1.632653061 = -1.735653996 Simplifying t + -1.632653061 = -1.735653996 Reorder the terms: -1.632653061 + t = -1.735653996 Solving -1.632653061 + t = -1.735653996 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -1.735653996 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -1.735653996 + 1.632653061 t = -1.735653996 + 1.632653061 Combine like terms: -1.735653996 + 1.632653061 = -0.103000935 t = -0.103000935 Simplifying t = -0.103000935Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.368307057, -0.103000935}
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