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Simplifying 2t2 + 14t + -22.5 = 0 Reorder the terms: -22.5 + 14t + 2t2 = 0 Solving -22.5 + 14t + 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'. -11.25 + 7t + t2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 7t + 11.25 + t2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 7t + t2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 7t + t2 = 0 + 11.25 7t + t2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 7t + t2 = 11.25 The t term is 7t. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7t + 12.25 + t2 = 11.25 + 12.25 Reorder the terms: 12.25 + 7t + t2 = 11.25 + 12.25 Combine like terms: 11.25 + 12.25 = 23.5 12.25 + 7t + t2 = 23.5 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (t + 3.5) equal to 4.847679857 and -4.847679857.Subproblem 1
t + 3.5 = 4.847679857 Simplifying t + 3.5 = 4.847679857 Reorder the terms: 3.5 + t = 4.847679857 Solving 3.5 + t = 4.847679857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = 4.847679857 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = 4.847679857 + -3.5 t = 4.847679857 + -3.5 Combine like terms: 4.847679857 + -3.5 = 1.347679857 t = 1.347679857 Simplifying t = 1.347679857Subproblem 2
t + 3.5 = -4.847679857 Simplifying t + 3.5 = -4.847679857 Reorder the terms: 3.5 + t = -4.847679857 Solving 3.5 + t = -4.847679857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = -4.847679857 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = -4.847679857 + -3.5 t = -4.847679857 + -3.5 Combine like terms: -4.847679857 + -3.5 = -8.347679857 t = -8.347679857 Simplifying t = -8.347679857Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.347679857, -8.347679857}
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