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Simplifying 36t2 + 79t + 5 = 0 Reorder the terms: 5 + 79t + 36t2 = 0 Solving 5 + 79t + 36t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.1388888889 + 2.194444444t + t2 = 0 Move the constant term to the right: Add '-0.1388888889' to each side of the equation. 0.1388888889 + 2.194444444t + -0.1388888889 + t2 = 0 + -0.1388888889 Reorder the terms: 0.1388888889 + -0.1388888889 + 2.194444444t + t2 = 0 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + 2.194444444t + t2 = 0 + -0.1388888889 2.194444444t + t2 = 0 + -0.1388888889 Combine like terms: 0 + -0.1388888889 = -0.1388888889 2.194444444t + t2 = -0.1388888889 The t term is 2.194444444t. Take half its coefficient (1.097222222). Square it (1.203896604) and add it to both sides. Add '1.203896604' to each side of the equation. 2.194444444t + 1.203896604 + t2 = -0.1388888889 + 1.203896604 Reorder the terms: 1.203896604 + 2.194444444t + t2 = -0.1388888889 + 1.203896604 Combine like terms: -0.1388888889 + 1.203896604 = 1.0650077151 1.203896604 + 2.194444444t + t2 = 1.0650077151 Factor a perfect square on the left side: (t + 1.097222222)(t + 1.097222222) = 1.0650077151 Calculate the square root of the right side: 1.03199211 Break this problem into two subproblems by setting (t + 1.097222222) equal to 1.03199211 and -1.03199211.Subproblem 1
t + 1.097222222 = 1.03199211 Simplifying t + 1.097222222 = 1.03199211 Reorder the terms: 1.097222222 + t = 1.03199211 Solving 1.097222222 + t = 1.03199211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.097222222' to each side of the equation. 1.097222222 + -1.097222222 + t = 1.03199211 + -1.097222222 Combine like terms: 1.097222222 + -1.097222222 = 0.000000000 0.000000000 + t = 1.03199211 + -1.097222222 t = 1.03199211 + -1.097222222 Combine like terms: 1.03199211 + -1.097222222 = -0.065230112 t = -0.065230112 Simplifying t = -0.065230112Subproblem 2
t + 1.097222222 = -1.03199211 Simplifying t + 1.097222222 = -1.03199211 Reorder the terms: 1.097222222 + t = -1.03199211 Solving 1.097222222 + t = -1.03199211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.097222222' to each side of the equation. 1.097222222 + -1.097222222 + t = -1.03199211 + -1.097222222 Combine like terms: 1.097222222 + -1.097222222 = 0.000000000 0.000000000 + t = -1.03199211 + -1.097222222 t = -1.03199211 + -1.097222222 Combine like terms: -1.03199211 + -1.097222222 = -2.129214332 t = -2.129214332 Simplifying t = -2.129214332Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.065230112, -2.129214332}
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