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Simplifying 9t2 + -46t + -130 = 0 Reorder the terms: -130 + -46t + 9t2 = 0 Solving -130 + -46t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -14.44444444 + -5.111111111t + t2 = 0 Move the constant term to the right: Add '14.44444444' to each side of the equation. -14.44444444 + -5.111111111t + 14.44444444 + t2 = 0 + 14.44444444 Reorder the terms: -14.44444444 + 14.44444444 + -5.111111111t + t2 = 0 + 14.44444444 Combine like terms: -14.44444444 + 14.44444444 = 0.00000000 0.00000000 + -5.111111111t + t2 = 0 + 14.44444444 -5.111111111t + t2 = 0 + 14.44444444 Combine like terms: 0 + 14.44444444 = 14.44444444 -5.111111111t + t2 = 14.44444444 The t term is -5.111111111t. Take half its coefficient (-2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. -5.111111111t + 6.530864200 + t2 = 14.44444444 + 6.530864200 Reorder the terms: 6.530864200 + -5.111111111t + t2 = 14.44444444 + 6.530864200 Combine like terms: 14.44444444 + 6.530864200 = 20.97530864 6.530864200 + -5.111111111t + t2 = 20.97530864 Factor a perfect square on the left side: (t + -2.555555556)(t + -2.555555556) = 20.97530864 Calculate the square root of the right side: 4.579880854 Break this problem into two subproblems by setting (t + -2.555555556) equal to 4.579880854 and -4.579880854.Subproblem 1
t + -2.555555556 = 4.579880854 Simplifying t + -2.555555556 = 4.579880854 Reorder the terms: -2.555555556 + t = 4.579880854 Solving -2.555555556 + t = 4.579880854 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + t = 4.579880854 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + t = 4.579880854 + 2.555555556 t = 4.579880854 + 2.555555556 Combine like terms: 4.579880854 + 2.555555556 = 7.13543641 t = 7.13543641 Simplifying t = 7.13543641Subproblem 2
t + -2.555555556 = -4.579880854 Simplifying t + -2.555555556 = -4.579880854 Reorder the terms: -2.555555556 + t = -4.579880854 Solving -2.555555556 + t = -4.579880854 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + t = -4.579880854 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + t = -4.579880854 + 2.555555556 t = -4.579880854 + 2.555555556 Combine like terms: -4.579880854 + 2.555555556 = -2.024325298 t = -2.024325298 Simplifying t = -2.024325298Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.13543641, -2.024325298}
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