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Simplifying -1.75t2 + 18.5t + -40.65 = 0 Reorder the terms: -40.65 + 18.5t + -1.75t2 = 0 Solving -40.65 + 18.5t + -1.75t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1.75 the coefficient of the squared term: Divide each side by '-1.75'. 23.22857143 + -10.57142857t + t2 = 0 Move the constant term to the right: Add '-23.22857143' to each side of the equation. 23.22857143 + -10.57142857t + -23.22857143 + t2 = 0 + -23.22857143 Reorder the terms: 23.22857143 + -23.22857143 + -10.57142857t + t2 = 0 + -23.22857143 Combine like terms: 23.22857143 + -23.22857143 = 0.00000000 0.00000000 + -10.57142857t + t2 = 0 + -23.22857143 -10.57142857t + t2 = 0 + -23.22857143 Combine like terms: 0 + -23.22857143 = -23.22857143 -10.57142857t + t2 = -23.22857143 The t term is -10.57142857t. Take half its coefficient (-5.285714285). Square it (27.93877550) and add it to both sides. Add '27.93877550' to each side of the equation. -10.57142857t + 27.93877550 + t2 = -23.22857143 + 27.93877550 Reorder the terms: 27.93877550 + -10.57142857t + t2 = -23.22857143 + 27.93877550 Combine like terms: -23.22857143 + 27.93877550 = 4.71020407 27.93877550 + -10.57142857t + t2 = 4.71020407 Factor a perfect square on the left side: (t + -5.285714285)(t + -5.285714285) = 4.71020407 Calculate the square root of the right side: 2.170300456 Break this problem into two subproblems by setting (t + -5.285714285) equal to 2.170300456 and -2.170300456.Subproblem 1
t + -5.285714285 = 2.170300456 Simplifying t + -5.285714285 = 2.170300456 Reorder the terms: -5.285714285 + t = 2.170300456 Solving -5.285714285 + t = 2.170300456 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.285714285' to each side of the equation. -5.285714285 + 5.285714285 + t = 2.170300456 + 5.285714285 Combine like terms: -5.285714285 + 5.285714285 = 0.000000000 0.000000000 + t = 2.170300456 + 5.285714285 t = 2.170300456 + 5.285714285 Combine like terms: 2.170300456 + 5.285714285 = 7.456014741 t = 7.456014741 Simplifying t = 7.456014741Subproblem 2
t + -5.285714285 = -2.170300456 Simplifying t + -5.285714285 = -2.170300456 Reorder the terms: -5.285714285 + t = -2.170300456 Solving -5.285714285 + t = -2.170300456 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.285714285' to each side of the equation. -5.285714285 + 5.285714285 + t = -2.170300456 + 5.285714285 Combine like terms: -5.285714285 + 5.285714285 = 0.000000000 0.000000000 + t = -2.170300456 + 5.285714285 t = -2.170300456 + 5.285714285 Combine like terms: -2.170300456 + 5.285714285 = 3.115413829 t = 3.115413829 Simplifying t = 3.115413829Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.456014741, 3.115413829}
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