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Simplifying t2 + -220t + -2725 = 0 Reorder the terms: -2725 + -220t + t2 = 0 Solving -2725 + -220t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '2725' to each side of the equation. -2725 + -220t + 2725 + t2 = 0 + 2725 Reorder the terms: -2725 + 2725 + -220t + t2 = 0 + 2725 Combine like terms: -2725 + 2725 = 0 0 + -220t + t2 = 0 + 2725 -220t + t2 = 0 + 2725 Combine like terms: 0 + 2725 = 2725 -220t + t2 = 2725 The t term is -220t. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220t + 12100 + t2 = 2725 + 12100 Reorder the terms: 12100 + -220t + t2 = 2725 + 12100 Combine like terms: 2725 + 12100 = 14825 12100 + -220t + t2 = 14825 Factor a perfect square on the left side: (t + -110)(t + -110) = 14825 Calculate the square root of the right side: 121.757956619 Break this problem into two subproblems by setting (t + -110) equal to 121.757956619 and -121.757956619.Subproblem 1
t + -110 = 121.757956619 Simplifying t + -110 = 121.757956619 Reorder the terms: -110 + t = 121.757956619 Solving -110 + t = 121.757956619 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + t = 121.757956619 + 110 Combine like terms: -110 + 110 = 0 0 + t = 121.757956619 + 110 t = 121.757956619 + 110 Combine like terms: 121.757956619 + 110 = 231.757956619 t = 231.757956619 Simplifying t = 231.757956619Subproblem 2
t + -110 = -121.757956619 Simplifying t + -110 = -121.757956619 Reorder the terms: -110 + t = -121.757956619 Solving -110 + t = -121.757956619 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + t = -121.757956619 + 110 Combine like terms: -110 + 110 = 0 0 + t = -121.757956619 + 110 t = -121.757956619 + 110 Combine like terms: -121.757956619 + 110 = -11.757956619 t = -11.757956619 Simplifying t = -11.757956619Solution
The solution to the problem is based on the solutions from the subproblems. t = {231.757956619, -11.757956619}
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