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Simplifying -4.9t2 + 45.083t + -18.3 = 0 Reorder the terms: -18.3 + 45.083t + -4.9t2 = 0 Solving -18.3 + 45.083t + -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'. 3.734693878 + -9.200612245t + t2 = 0 Move the constant term to the right: Add '-3.734693878' to each side of the equation. 3.734693878 + -9.200612245t + -3.734693878 + t2 = 0 + -3.734693878 Reorder the terms: 3.734693878 + -3.734693878 + -9.200612245t + t2 = 0 + -3.734693878 Combine like terms: 3.734693878 + -3.734693878 = 0.000000000 0.000000000 + -9.200612245t + t2 = 0 + -3.734693878 -9.200612245t + t2 = 0 + -3.734693878 Combine like terms: 0 + -3.734693878 = -3.734693878 -9.200612245t + t2 = -3.734693878 The t term is -9.200612245t. Take half its coefficient (-4.600306123). Square it (21.16281643) and add it to both sides. Add '21.16281643' to each side of the equation. -9.200612245t + 21.16281643 + t2 = -3.734693878 + 21.16281643 Reorder the terms: 21.16281643 + -9.200612245t + t2 = -3.734693878 + 21.16281643 Combine like terms: -3.734693878 + 21.16281643 = 17.428122552 21.16281643 + -9.200612245t + t2 = 17.428122552 Factor a perfect square on the left side: (t + -4.600306123)(t + -4.600306123) = 17.428122552 Calculate the square root of the right side: 4.174700295 Break this problem into two subproblems by setting (t + -4.600306123) equal to 4.174700295 and -4.174700295.Subproblem 1
t + -4.600306123 = 4.174700295 Simplifying t + -4.600306123 = 4.174700295 Reorder the terms: -4.600306123 + t = 4.174700295 Solving -4.600306123 + t = 4.174700295 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.600306123' to each side of the equation. -4.600306123 + 4.600306123 + t = 4.174700295 + 4.600306123 Combine like terms: -4.600306123 + 4.600306123 = 0.000000000 0.000000000 + t = 4.174700295 + 4.600306123 t = 4.174700295 + 4.600306123 Combine like terms: 4.174700295 + 4.600306123 = 8.775006418 t = 8.775006418 Simplifying t = 8.775006418Subproblem 2
t + -4.600306123 = -4.174700295 Simplifying t + -4.600306123 = -4.174700295 Reorder the terms: -4.600306123 + t = -4.174700295 Solving -4.600306123 + t = -4.174700295 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.600306123' to each side of the equation. -4.600306123 + 4.600306123 + t = -4.174700295 + 4.600306123 Combine like terms: -4.600306123 + 4.600306123 = 0.000000000 0.000000000 + t = -4.174700295 + 4.600306123 t = -4.174700295 + 4.600306123 Combine like terms: -4.174700295 + 4.600306123 = 0.425605828 t = 0.425605828 Simplifying t = 0.425605828Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.775006418, 0.425605828}
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