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Simplifying 2t2 + 9t + -7 = 0 Reorder the terms: -7 + 9t + 2t2 = 0 Solving -7 + 9t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 4.5t + t2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 4.5t + 3.5 + t2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 4.5t + t2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 4.5t + t2 = 0 + 3.5 4.5t + t2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 4.5t + t2 = 3.5 The t term is 4.5t. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5t + 5.0625 + t2 = 3.5 + 5.0625 Reorder the terms: 5.0625 + 4.5t + t2 = 3.5 + 5.0625 Combine like terms: 3.5 + 5.0625 = 8.5625 5.0625 + 4.5t + t2 = 8.5625 Factor a perfect square on the left side: (t + 2.25)(t + 2.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (t + 2.25) equal to 2.926174978 and -2.926174978.Subproblem 1
t + 2.25 = 2.926174978 Simplifying t + 2.25 = 2.926174978 Reorder the terms: 2.25 + t = 2.926174978 Solving 2.25 + t = 2.926174978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + t = 2.926174978 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + t = 2.926174978 + -2.25 t = 2.926174978 + -2.25 Combine like terms: 2.926174978 + -2.25 = 0.676174978 t = 0.676174978 Simplifying t = 0.676174978Subproblem 2
t + 2.25 = -2.926174978 Simplifying t + 2.25 = -2.926174978 Reorder the terms: 2.25 + t = -2.926174978 Solving 2.25 + t = -2.926174978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + t = -2.926174978 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + t = -2.926174978 + -2.25 t = -2.926174978 + -2.25 Combine like terms: -2.926174978 + -2.25 = -5.176174978 t = -5.176174978 Simplifying t = -5.176174978Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.676174978, -5.176174978}
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