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Simplifying -1.75t2 + 20.5t + -50.65 = 0 Reorder the terms: -50.65 + 20.5t + -1.75t2 = 0 Solving -50.65 + 20.5t + -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'. 28.94285714 + -11.71428571t + t2 = 0 Move the constant term to the right: Add '-28.94285714' to each side of the equation. 28.94285714 + -11.71428571t + -28.94285714 + t2 = 0 + -28.94285714 Reorder the terms: 28.94285714 + -28.94285714 + -11.71428571t + t2 = 0 + -28.94285714 Combine like terms: 28.94285714 + -28.94285714 = 0.00000000 0.00000000 + -11.71428571t + t2 = 0 + -28.94285714 -11.71428571t + t2 = 0 + -28.94285714 Combine like terms: 0 + -28.94285714 = -28.94285714 -11.71428571t + t2 = -28.94285714 The t term is -11.71428571t. Take half its coefficient (-5.857142855). Square it (34.30612242) and add it to both sides. Add '34.30612242' to each side of the equation. -11.71428571t + 34.30612242 + t2 = -28.94285714 + 34.30612242 Reorder the terms: 34.30612242 + -11.71428571t + t2 = -28.94285714 + 34.30612242 Combine like terms: -28.94285714 + 34.30612242 = 5.36326528 34.30612242 + -11.71428571t + t2 = 5.36326528 Factor a perfect square on the left side: (t + -5.857142855)(t + -5.857142855) = 5.36326528 Calculate the square root of the right side: 2.315872466 Break this problem into two subproblems by setting (t + -5.857142855) equal to 2.315872466 and -2.315872466.Subproblem 1
t + -5.857142855 = 2.315872466 Simplifying t + -5.857142855 = 2.315872466 Reorder the terms: -5.857142855 + t = 2.315872466 Solving -5.857142855 + t = 2.315872466 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.857142855' to each side of the equation. -5.857142855 + 5.857142855 + t = 2.315872466 + 5.857142855 Combine like terms: -5.857142855 + 5.857142855 = 0.000000000 0.000000000 + t = 2.315872466 + 5.857142855 t = 2.315872466 + 5.857142855 Combine like terms: 2.315872466 + 5.857142855 = 8.173015321 t = 8.173015321 Simplifying t = 8.173015321Subproblem 2
t + -5.857142855 = -2.315872466 Simplifying t + -5.857142855 = -2.315872466 Reorder the terms: -5.857142855 + t = -2.315872466 Solving -5.857142855 + t = -2.315872466 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.857142855' to each side of the equation. -5.857142855 + 5.857142855 + t = -2.315872466 + 5.857142855 Combine like terms: -5.857142855 + 5.857142855 = 0.000000000 0.000000000 + t = -2.315872466 + 5.857142855 t = -2.315872466 + 5.857142855 Combine like terms: -2.315872466 + 5.857142855 = 3.541270389 t = 3.541270389 Simplifying t = 3.541270389Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.173015321, 3.541270389}
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