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Simplifying t2 + -18t + 40.5 = 0 Reorder the terms: 40.5 + -18t + t2 = 0 Solving 40.5 + -18t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + -18t + -40.5 + t2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + -18t + t2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + -18t + t2 = 0 + -40.5 -18t + t2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 -18t + t2 = -40.5 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = -40.5 + 81 Reorder the terms: 81 + -18t + t2 = -40.5 + 81 Combine like terms: -40.5 + 81 = 40.5 81 + -18t + t2 = 40.5 Factor a perfect square on the left side: (t + -9)(t + -9) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (t + -9) equal to 6.363961031 and -6.363961031.Subproblem 1
t + -9 = 6.363961031 Simplifying t + -9 = 6.363961031 Reorder the terms: -9 + t = 6.363961031 Solving -9 + t = 6.363961031 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 6.363961031 + 9 Combine like terms: -9 + 9 = 0 0 + t = 6.363961031 + 9 t = 6.363961031 + 9 Combine like terms: 6.363961031 + 9 = 15.363961031 t = 15.363961031 Simplifying t = 15.363961031Subproblem 2
t + -9 = -6.363961031 Simplifying t + -9 = -6.363961031 Reorder the terms: -9 + t = -6.363961031 Solving -9 + t = -6.363961031 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -6.363961031 + 9 Combine like terms: -9 + 9 = 0 0 + t = -6.363961031 + 9 t = -6.363961031 + 9 Combine like terms: -6.363961031 + 9 = 2.636038969 t = 2.636038969 Simplifying t = 2.636038969Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.363961031, 2.636038969}
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