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Simplifying -4.9t2 + 32t + 40 = 0 Reorder the terms: 40 + 32t + -4.9t2 = 0 Solving 40 + 32t + -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'. -8.163265306 + -6.530612245t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -6.530612245t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -6.530612245t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -6.530612245t + t2 = 0 + 8.163265306 -6.530612245t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -6.530612245t + t2 = 8.163265306 The t term is -6.530612245t. Take half its coefficient (-3.265306123). Square it (10.66222408) and add it to both sides. Add '10.66222408' to each side of the equation. -6.530612245t + 10.66222408 + t2 = 8.163265306 + 10.66222408 Reorder the terms: 10.66222408 + -6.530612245t + t2 = 8.163265306 + 10.66222408 Combine like terms: 8.163265306 + 10.66222408 = 18.825489386 10.66222408 + -6.530612245t + t2 = 18.825489386 Factor a perfect square on the left side: (t + -3.265306123)(t + -3.265306123) = 18.825489386 Calculate the square root of the right side: 4.338835026 Break this problem into two subproblems by setting (t + -3.265306123) equal to 4.338835026 and -4.338835026.Subproblem 1
t + -3.265306123 = 4.338835026 Simplifying t + -3.265306123 = 4.338835026 Reorder the terms: -3.265306123 + t = 4.338835026 Solving -3.265306123 + t = 4.338835026 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + t = 4.338835026 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + t = 4.338835026 + 3.265306123 t = 4.338835026 + 3.265306123 Combine like terms: 4.338835026 + 3.265306123 = 7.604141149 t = 7.604141149 Simplifying t = 7.604141149Subproblem 2
t + -3.265306123 = -4.338835026 Simplifying t + -3.265306123 = -4.338835026 Reorder the terms: -3.265306123 + t = -4.338835026 Solving -3.265306123 + t = -4.338835026 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.265306123' to each side of the equation. -3.265306123 + 3.265306123 + t = -4.338835026 + 3.265306123 Combine like terms: -3.265306123 + 3.265306123 = 0.000000000 0.000000000 + t = -4.338835026 + 3.265306123 t = -4.338835026 + 3.265306123 Combine like terms: -4.338835026 + 3.265306123 = -1.073528903 t = -1.073528903 Simplifying t = -1.073528903Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.604141149, -1.073528903}
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