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Simplifying t2 + -198t + 5184 = 0 Reorder the terms: 5184 + -198t + t2 = 0 Solving 5184 + -198t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-5184' to each side of the equation. 5184 + -198t + -5184 + t2 = 0 + -5184 Reorder the terms: 5184 + -5184 + -198t + t2 = 0 + -5184 Combine like terms: 5184 + -5184 = 0 0 + -198t + t2 = 0 + -5184 -198t + t2 = 0 + -5184 Combine like terms: 0 + -5184 = -5184 -198t + t2 = -5184 The t term is -198t. Take half its coefficient (-99). Square it (9801) and add it to both sides. Add '9801' to each side of the equation. -198t + 9801 + t2 = -5184 + 9801 Reorder the terms: 9801 + -198t + t2 = -5184 + 9801 Combine like terms: -5184 + 9801 = 4617 9801 + -198t + t2 = 4617 Factor a perfect square on the left side: (t + -99)(t + -99) = 4617 Calculate the square root of the right side: 67.948509917 Break this problem into two subproblems by setting (t + -99) equal to 67.948509917 and -67.948509917.Subproblem 1
t + -99 = 67.948509917 Simplifying t + -99 = 67.948509917 Reorder the terms: -99 + t = 67.948509917 Solving -99 + t = 67.948509917 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '99' to each side of the equation. -99 + 99 + t = 67.948509917 + 99 Combine like terms: -99 + 99 = 0 0 + t = 67.948509917 + 99 t = 67.948509917 + 99 Combine like terms: 67.948509917 + 99 = 166.948509917 t = 166.948509917 Simplifying t = 166.948509917Subproblem 2
t + -99 = -67.948509917 Simplifying t + -99 = -67.948509917 Reorder the terms: -99 + t = -67.948509917 Solving -99 + t = -67.948509917 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '99' to each side of the equation. -99 + 99 + t = -67.948509917 + 99 Combine like terms: -99 + 99 = 0 0 + t = -67.948509917 + 99 t = -67.948509917 + 99 Combine like terms: -67.948509917 + 99 = 31.051490083 t = 31.051490083 Simplifying t = 31.051490083Solution
The solution to the problem is based on the solutions from the subproblems. t = {166.948509917, 31.051490083}
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