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Simplifying 9t2 = 36t + -1 Reorder the terms: 9t2 = -1 + 36t Solving 9t2 = -1 + 36t Solving for variable 't'. Reorder the terms: 1 + -36t + 9t2 = -1 + 36t + 1 + -36t Reorder the terms: 1 + -36t + 9t2 = -1 + 1 + 36t + -36t Combine like terms: -1 + 1 = 0 1 + -36t + 9t2 = 0 + 36t + -36t 1 + -36t + 9t2 = 36t + -36t Combine like terms: 36t + -36t = 0 1 + -36t + 9t2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -4t + t2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -4t + -0.1111111111 + t2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -4t + t2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -4t + t2 = 0 + -0.1111111111 -4t + t2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -4t + t2 = -0.1111111111 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -0.1111111111 + 4 Reorder the terms: 4 + -4t + t2 = -0.1111111111 + 4 Combine like terms: -0.1111111111 + 4 = 3.8888888889 4 + -4t + t2 = 3.8888888889 Factor a perfect square on the left side: (t + -2)(t + -2) = 3.8888888889 Calculate the square root of the right side: 1.972026594 Break this problem into two subproblems by setting (t + -2) equal to 1.972026594 and -1.972026594.Subproblem 1
t + -2 = 1.972026594 Simplifying t + -2 = 1.972026594 Reorder the terms: -2 + t = 1.972026594 Solving -2 + t = 1.972026594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.972026594 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.972026594 + 2 t = 1.972026594 + 2 Combine like terms: 1.972026594 + 2 = 3.972026594 t = 3.972026594 Simplifying t = 3.972026594Subproblem 2
t + -2 = -1.972026594 Simplifying t + -2 = -1.972026594 Reorder the terms: -2 + t = -1.972026594 Solving -2 + t = -1.972026594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.972026594 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.972026594 + 2 t = -1.972026594 + 2 Combine like terms: -1.972026594 + 2 = 0.027973406 t = 0.027973406 Simplifying t = 0.027973406Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.972026594, 0.027973406}
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