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Simplifying t2 + 36t + 81 = 0 Reorder the terms: 81 + 36t + t2 = 0 Solving 81 + 36t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + 36t + -81 + t2 = 0 + -81 Reorder the terms: 81 + -81 + 36t + t2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 36t + t2 = 0 + -81 36t + t2 = 0 + -81 Combine like terms: 0 + -81 = -81 36t + t2 = -81 The t term is 36t. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36t + 324 + t2 = -81 + 324 Reorder the terms: 324 + 36t + t2 = -81 + 324 Combine like terms: -81 + 324 = 243 324 + 36t + t2 = 243 Factor a perfect square on the left side: (t + 18)(t + 18) = 243 Calculate the square root of the right side: 15.588457268 Break this problem into two subproblems by setting (t + 18) equal to 15.588457268 and -15.588457268.Subproblem 1
t + 18 = 15.588457268 Simplifying t + 18 = 15.588457268 Reorder the terms: 18 + t = 15.588457268 Solving 18 + t = 15.588457268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + t = 15.588457268 + -18 Combine like terms: 18 + -18 = 0 0 + t = 15.588457268 + -18 t = 15.588457268 + -18 Combine like terms: 15.588457268 + -18 = -2.411542732 t = -2.411542732 Simplifying t = -2.411542732Subproblem 2
t + 18 = -15.588457268 Simplifying t + 18 = -15.588457268 Reorder the terms: 18 + t = -15.588457268 Solving 18 + t = -15.588457268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + t = -15.588457268 + -18 Combine like terms: 18 + -18 = 0 0 + t = -15.588457268 + -18 t = -15.588457268 + -18 Combine like terms: -15.588457268 + -18 = -33.588457268 t = -33.588457268 Simplifying t = -33.588457268Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.411542732, -33.588457268}
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