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Simplifying t2 + -90t + -1100 = 0 Reorder the terms: -1100 + -90t + t2 = 0 Solving -1100 + -90t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1100' to each side of the equation. -1100 + -90t + 1100 + t2 = 0 + 1100 Reorder the terms: -1100 + 1100 + -90t + t2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + -90t + t2 = 0 + 1100 -90t + t2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 -90t + t2 = 1100 The t term is -90t. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90t + 2025 + t2 = 1100 + 2025 Reorder the terms: 2025 + -90t + t2 = 1100 + 2025 Combine like terms: 1100 + 2025 = 3125 2025 + -90t + t2 = 3125 Factor a perfect square on the left side: (t + -45)(t + -45) = 3125 Calculate the square root of the right side: 55.901699437 Break this problem into two subproblems by setting (t + -45) equal to 55.901699437 and -55.901699437.Subproblem 1
t + -45 = 55.901699437 Simplifying t + -45 = 55.901699437 Reorder the terms: -45 + t = 55.901699437 Solving -45 + t = 55.901699437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + t = 55.901699437 + 45 Combine like terms: -45 + 45 = 0 0 + t = 55.901699437 + 45 t = 55.901699437 + 45 Combine like terms: 55.901699437 + 45 = 100.901699437 t = 100.901699437 Simplifying t = 100.901699437Subproblem 2
t + -45 = -55.901699437 Simplifying t + -45 = -55.901699437 Reorder the terms: -45 + t = -55.901699437 Solving -45 + t = -55.901699437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + t = -55.901699437 + 45 Combine like terms: -45 + 45 = 0 0 + t = -55.901699437 + 45 t = -55.901699437 + 45 Combine like terms: -55.901699437 + 45 = -10.901699437 t = -10.901699437 Simplifying t = -10.901699437Solution
The solution to the problem is based on the solutions from the subproblems. t = {100.901699437, -10.901699437}
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