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Simplifying 100 = 81t + -9t2 Solving 100 = 81t + -9t2 Solving for variable 't'. Reorder the terms: 100 + -81t + 9t2 = 81t + -81t + -9t2 + 9t2 Combine like terms: 81t + -81t = 0 100 + -81t + 9t2 = 0 + -9t2 + 9t2 100 + -81t + 9t2 = -9t2 + 9t2 Combine like terms: -9t2 + 9t2 = 0 100 + -81t + 9t2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 11.11111111 + -9t + t2 = 0 Move the constant term to the right: Add '-11.11111111' to each side of the equation. 11.11111111 + -9t + -11.11111111 + t2 = 0 + -11.11111111 Reorder the terms: 11.11111111 + -11.11111111 + -9t + t2 = 0 + -11.11111111 Combine like terms: 11.11111111 + -11.11111111 = 0.00000000 0.00000000 + -9t + t2 = 0 + -11.11111111 -9t + t2 = 0 + -11.11111111 Combine like terms: 0 + -11.11111111 = -11.11111111 -9t + t2 = -11.11111111 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -11.11111111 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -11.11111111 + 20.25 Combine like terms: -11.11111111 + 20.25 = 9.13888889 20.25 + -9t + t2 = 9.13888889 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 9.13888889 Calculate the square root of the right side: 3.023059525 Break this problem into two subproblems by setting (t + -4.5) equal to 3.023059525 and -3.023059525.Subproblem 1
t + -4.5 = 3.023059525 Simplifying t + -4.5 = 3.023059525 Reorder the terms: -4.5 + t = 3.023059525 Solving -4.5 + t = 3.023059525 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 3.023059525 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 3.023059525 + 4.5 t = 3.023059525 + 4.5 Combine like terms: 3.023059525 + 4.5 = 7.523059525 t = 7.523059525 Simplifying t = 7.523059525Subproblem 2
t + -4.5 = -3.023059525 Simplifying t + -4.5 = -3.023059525 Reorder the terms: -4.5 + t = -3.023059525 Solving -4.5 + t = -3.023059525 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -3.023059525 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -3.023059525 + 4.5 t = -3.023059525 + 4.5 Combine like terms: -3.023059525 + 4.5 = 1.476940475 t = 1.476940475 Simplifying t = 1.476940475Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.523059525, 1.476940475}
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