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Simplifying 2425t2 + -12150t + -231775 = 0 Reorder the terms: -231775 + -12150t + 2425t2 = 0 Solving -231775 + -12150t + 2425t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '25'. 25(-9271 + -486t + 97t2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-9271 + -486t + 97t2)' equal to zero and attempt to solve: Simplifying -9271 + -486t + 97t2 = 0 Solving -9271 + -486t + 97t2 = 0 Begin completing the square. Divide all terms by 97 the coefficient of the squared term: Divide each side by '97'. -95.57731959 + -5.010309278t + t2 = 0 Move the constant term to the right: Add '95.57731959' to each side of the equation. -95.57731959 + -5.010309278t + 95.57731959 + t2 = 0 + 95.57731959 Reorder the terms: -95.57731959 + 95.57731959 + -5.010309278t + t2 = 0 + 95.57731959 Combine like terms: -95.57731959 + 95.57731959 = 0.00000000 0.00000000 + -5.010309278t + t2 = 0 + 95.57731959 -5.010309278t + t2 = 0 + 95.57731959 Combine like terms: 0 + 95.57731959 = 95.57731959 -5.010309278t + t2 = 95.57731959 The t term is -5.010309278t. Take half its coefficient (-2.505154639). Square it (6.275799765) and add it to both sides. Add '6.275799765' to each side of the equation. -5.010309278t + 6.275799765 + t2 = 95.57731959 + 6.275799765 Reorder the terms: 6.275799765 + -5.010309278t + t2 = 95.57731959 + 6.275799765 Combine like terms: 95.57731959 + 6.275799765 = 101.853119355 6.275799765 + -5.010309278t + t2 = 101.853119355 Factor a perfect square on the left side: (t + -2.505154639)(t + -2.505154639) = 101.853119355 Calculate the square root of the right side: 10.092230643 Break this problem into two subproblems by setting (t + -2.505154639) equal to 10.092230643 and -10.092230643.Subproblem 1
t + -2.505154639 = 10.092230643 Simplifying t + -2.505154639 = 10.092230643 Reorder the terms: -2.505154639 + t = 10.092230643 Solving -2.505154639 + t = 10.092230643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.505154639' to each side of the equation. -2.505154639 + 2.505154639 + t = 10.092230643 + 2.505154639 Combine like terms: -2.505154639 + 2.505154639 = 0.000000000 0.000000000 + t = 10.092230643 + 2.505154639 t = 10.092230643 + 2.505154639 Combine like terms: 10.092230643 + 2.505154639 = 12.597385282 t = 12.597385282 Simplifying t = 12.597385282Subproblem 2
t + -2.505154639 = -10.092230643 Simplifying t + -2.505154639 = -10.092230643 Reorder the terms: -2.505154639 + t = -10.092230643 Solving -2.505154639 + t = -10.092230643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.505154639' to each side of the equation. -2.505154639 + 2.505154639 + t = -10.092230643 + 2.505154639 Combine like terms: -2.505154639 + 2.505154639 = 0.000000000 0.000000000 + t = -10.092230643 + 2.505154639 t = -10.092230643 + 2.505154639 Combine like terms: -10.092230643 + 2.505154639 = -7.587076004 t = -7.587076004 Simplifying t = -7.587076004Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.597385282, -7.587076004}Solution
t = {12.597385282, -7.587076004}
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