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Simplifying -9t2 = 18t + 7 Reorder the terms: -9t2 = 7 + 18t Solving -9t2 = 7 + 18t Solving for variable 't'. Reorder the terms: -7 + -18t + -9t2 = 7 + 18t + -7 + -18t Reorder the terms: -7 + -18t + -9t2 = 7 + -7 + 18t + -18t Combine like terms: 7 + -7 = 0 -7 + -18t + -9t2 = 0 + 18t + -18t -7 + -18t + -9t2 = 18t + -18t Combine like terms: 18t + -18t = 0 -7 + -18t + -9t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 18t + 9t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 18t + 9t2)' equal to zero and attempt to solve: Simplifying 7 + 18t + 9t2 = 0 Solving 7 + 18t + 9t2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 2t + t2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 2t + -0.7777777778 + t2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 2t + t2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 2t + t2 = 0 + -0.7777777778 2t + t2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 2t + t2 = -0.7777777778 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -0.7777777778 + 1 Reorder the terms: 1 + 2t + t2 = -0.7777777778 + 1 Combine like terms: -0.7777777778 + 1 = 0.2222222222 1 + 2t + t2 = 0.2222222222 Factor a perfect square on the left side: (t + 1)(t + 1) = 0.2222222222 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (t + 1) equal to 0.471404521 and -0.471404521.Subproblem 1
t + 1 = 0.471404521 Simplifying t + 1 = 0.471404521 Reorder the terms: 1 + t = 0.471404521 Solving 1 + t = 0.471404521 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0.471404521 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0.471404521 + -1 t = 0.471404521 + -1 Combine like terms: 0.471404521 + -1 = -0.528595479 t = -0.528595479 Simplifying t = -0.528595479Subproblem 2
t + 1 = -0.471404521 Simplifying t + 1 = -0.471404521 Reorder the terms: 1 + t = -0.471404521 Solving 1 + t = -0.471404521 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -0.471404521 + -1 Combine like terms: 1 + -1 = 0 0 + t = -0.471404521 + -1 t = -0.471404521 + -1 Combine like terms: -0.471404521 + -1 = -1.471404521 t = -1.471404521 Simplifying t = -1.471404521Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.528595479, -1.471404521}Solution
t = {-0.528595479, -1.471404521}
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