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Simplifying 5t2 + 9t + -19 = 0 Reorder the terms: -19 + 9t + 5t2 = 0 Solving -19 + 9t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + 1.8t + t2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 1.8t + 3.8 + t2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 1.8t + t2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 1.8t + t2 = 0 + 3.8 1.8t + t2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 1.8t + t2 = 3.8 The t term is 1.8t. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8t + 0.81 + t2 = 3.8 + 0.81 Reorder the terms: 0.81 + 1.8t + t2 = 3.8 + 0.81 Combine like terms: 3.8 + 0.81 = 4.61 0.81 + 1.8t + t2 = 4.61 Factor a perfect square on the left side: (t + 0.9)(t + 0.9) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (t + 0.9) equal to 2.147091055 and -2.147091055.Subproblem 1
t + 0.9 = 2.147091055 Simplifying t + 0.9 = 2.147091055 Reorder the terms: 0.9 + t = 2.147091055 Solving 0.9 + t = 2.147091055 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + t = 2.147091055 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + t = 2.147091055 + -0.9 t = 2.147091055 + -0.9 Combine like terms: 2.147091055 + -0.9 = 1.247091055 t = 1.247091055 Simplifying t = 1.247091055Subproblem 2
t + 0.9 = -2.147091055 Simplifying t + 0.9 = -2.147091055 Reorder the terms: 0.9 + t = -2.147091055 Solving 0.9 + t = -2.147091055 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + t = -2.147091055 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + t = -2.147091055 + -0.9 t = -2.147091055 + -0.9 Combine like terms: -2.147091055 + -0.9 = -3.047091055 t = -3.047091055 Simplifying t = -3.047091055Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.247091055, -3.047091055}
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