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Simplifying t2 + -19t + 4 = 0 Reorder the terms: 4 + -19t + t2 = 0 Solving 4 + -19t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -19t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -19t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -19t + t2 = 0 + -4 -19t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -19t + t2 = -4 The t term is -19t. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19t + 90.25 + t2 = -4 + 90.25 Reorder the terms: 90.25 + -19t + t2 = -4 + 90.25 Combine like terms: -4 + 90.25 = 86.25 90.25 + -19t + t2 = 86.25 Factor a perfect square on the left side: (t + -9.5)(t + -9.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (t + -9.5) equal to 9.287087811 and -9.287087811.Subproblem 1
t + -9.5 = 9.287087811 Simplifying t + -9.5 = 9.287087811 Reorder the terms: -9.5 + t = 9.287087811 Solving -9.5 + t = 9.287087811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + t = 9.287087811 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + t = 9.287087811 + 9.5 t = 9.287087811 + 9.5 Combine like terms: 9.287087811 + 9.5 = 18.787087811 t = 18.787087811 Simplifying t = 18.787087811Subproblem 2
t + -9.5 = -9.287087811 Simplifying t + -9.5 = -9.287087811 Reorder the terms: -9.5 + t = -9.287087811 Solving -9.5 + t = -9.287087811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + t = -9.287087811 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + t = -9.287087811 + 9.5 t = -9.287087811 + 9.5 Combine like terms: -9.287087811 + 9.5 = 0.212912189 t = 0.212912189 Simplifying t = 0.212912189Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.787087811, 0.212912189}
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