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Simplifying 1.75t2 + -34.5t + -241.5 = 0 Reorder the terms: -241.5 + -34.5t + 1.75t2 = 0 Solving -241.5 + -34.5t + 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'. -138 + -19.71428571t + t2 = 0 Move the constant term to the right: Add '138' to each side of the equation. -138 + -19.71428571t + 138 + t2 = 0 + 138 Reorder the terms: -138 + 138 + -19.71428571t + t2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + -19.71428571t + t2 = 0 + 138 -19.71428571t + t2 = 0 + 138 Combine like terms: 0 + 138 = 138 -19.71428571t + t2 = 138 The t term is -19.71428571t. Take half its coefficient (-9.857142855). Square it (97.16326526) and add it to both sides. Add '97.16326526' to each side of the equation. -19.71428571t + 97.16326526 + t2 = 138 + 97.16326526 Reorder the terms: 97.16326526 + -19.71428571t + t2 = 138 + 97.16326526 Combine like terms: 138 + 97.16326526 = 235.16326526 97.16326526 + -19.71428571t + t2 = 235.16326526 Factor a perfect square on the left side: (t + -9.857142855)(t + -9.857142855) = 235.16326526 Calculate the square root of the right side: 15.335033918 Break this problem into two subproblems by setting (t + -9.857142855) equal to 15.335033918 and -15.335033918.Subproblem 1
t + -9.857142855 = 15.335033918 Simplifying t + -9.857142855 = 15.335033918 Reorder the terms: -9.857142855 + t = 15.335033918 Solving -9.857142855 + t = 15.335033918 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.857142855' to each side of the equation. -9.857142855 + 9.857142855 + t = 15.335033918 + 9.857142855 Combine like terms: -9.857142855 + 9.857142855 = 0.000000000 0.000000000 + t = 15.335033918 + 9.857142855 t = 15.335033918 + 9.857142855 Combine like terms: 15.335033918 + 9.857142855 = 25.192176773 t = 25.192176773 Simplifying t = 25.192176773Subproblem 2
t + -9.857142855 = -15.335033918 Simplifying t + -9.857142855 = -15.335033918 Reorder the terms: -9.857142855 + t = -15.335033918 Solving -9.857142855 + t = -15.335033918 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.857142855' to each side of the equation. -9.857142855 + 9.857142855 + t = -15.335033918 + 9.857142855 Combine like terms: -9.857142855 + 9.857142855 = 0.000000000 0.000000000 + t = -15.335033918 + 9.857142855 t = -15.335033918 + 9.857142855 Combine like terms: -15.335033918 + 9.857142855 = -5.477891063 t = -5.477891063 Simplifying t = -5.477891063Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.192176773, -5.477891063}
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