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Simplifying -4t2 + 18t + 81 = 0 Reorder the terms: 81 + 18t + -4t2 = 0 Solving 81 + 18t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -20.25 + -4.5t + t2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -4.5t + 20.25 + t2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -4.5t + t2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -4.5t + t2 = 0 + 20.25 -4.5t + t2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -4.5t + t2 = 20.25 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 20.25 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 20.25 + 5.0625 Combine like terms: 20.25 + 5.0625 = 25.3125 5.0625 + -4.5t + t2 = 25.3125 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 25.3125 Calculate the square root of the right side: 5.031152949 Break this problem into two subproblems by setting (t + -2.25) equal to 5.031152949 and -5.031152949.Subproblem 1
t + -2.25 = 5.031152949 Simplifying t + -2.25 = 5.031152949 Reorder the terms: -2.25 + t = 5.031152949 Solving -2.25 + t = 5.031152949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 5.031152949 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 5.031152949 + 2.25 t = 5.031152949 + 2.25 Combine like terms: 5.031152949 + 2.25 = 7.281152949 t = 7.281152949 Simplifying t = 7.281152949Subproblem 2
t + -2.25 = -5.031152949 Simplifying t + -2.25 = -5.031152949 Reorder the terms: -2.25 + t = -5.031152949 Solving -2.25 + t = -5.031152949 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -5.031152949 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -5.031152949 + 2.25 t = -5.031152949 + 2.25 Combine like terms: -5.031152949 + 2.25 = -2.781152949 t = -2.781152949 Simplifying t = -2.781152949Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.281152949, -2.781152949}
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