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Simplifying t2 + -45t + -36 = 0 Reorder the terms: -36 + -45t + t2 = 0 Solving -36 + -45t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -45t + 36 + t2 = 0 + 36 Reorder the terms: -36 + 36 + -45t + t2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -45t + t2 = 0 + 36 -45t + t2 = 0 + 36 Combine like terms: 0 + 36 = 36 -45t + t2 = 36 The t term is -45t. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45t + 506.25 + t2 = 36 + 506.25 Reorder the terms: 506.25 + -45t + t2 = 36 + 506.25 Combine like terms: 36 + 506.25 = 542.25 506.25 + -45t + t2 = 542.25 Factor a perfect square on the left side: (t + -22.5)(t + -22.5) = 542.25 Calculate the square root of the right side: 23.286262044 Break this problem into two subproblems by setting (t + -22.5) equal to 23.286262044 and -23.286262044.Subproblem 1
t + -22.5 = 23.286262044 Simplifying t + -22.5 = 23.286262044 Reorder the terms: -22.5 + t = 23.286262044 Solving -22.5 + t = 23.286262044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + t = 23.286262044 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + t = 23.286262044 + 22.5 t = 23.286262044 + 22.5 Combine like terms: 23.286262044 + 22.5 = 45.786262044 t = 45.786262044 Simplifying t = 45.786262044Subproblem 2
t + -22.5 = -23.286262044 Simplifying t + -22.5 = -23.286262044 Reorder the terms: -22.5 + t = -23.286262044 Solving -22.5 + t = -23.286262044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + t = -23.286262044 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + t = -23.286262044 + 22.5 t = -23.286262044 + 22.5 Combine like terms: -23.286262044 + 22.5 = -0.786262044 t = -0.786262044 Simplifying t = -0.786262044Solution
The solution to the problem is based on the solutions from the subproblems. t = {45.786262044, -0.786262044}
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