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Simplifying 30 = 2t2 + -6t + 7 Reorder the terms: 30 = 7 + -6t + 2t2 Solving 30 = 7 + -6t + 2t2 Solving for variable 't'. Combine like terms: 30 + -7 = 23 23 + 6t + -2t2 = 7 + -6t + 2t2 + -7 + 6t + -2t2 Reorder the terms: 23 + 6t + -2t2 = 7 + -7 + -6t + 6t + 2t2 + -2t2 Combine like terms: 7 + -7 = 0 23 + 6t + -2t2 = 0 + -6t + 6t + 2t2 + -2t2 23 + 6t + -2t2 = -6t + 6t + 2t2 + -2t2 Combine like terms: -6t + 6t = 0 23 + 6t + -2t2 = 0 + 2t2 + -2t2 23 + 6t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 23 + 6t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + -3t + t2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -3t + 11.5 + t2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -3t + t2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -3t + t2 = 0 + 11.5 -3t + t2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -3t + t2 = 11.5 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 11.5 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 11.5 + 2.25 Combine like terms: 11.5 + 2.25 = 13.75 2.25 + -3t + t2 = 13.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (t + -1.5) equal to 3.708099244 and -3.708099244.Subproblem 1
t + -1.5 = 3.708099244 Simplifying t + -1.5 = 3.708099244 Reorder the terms: -1.5 + t = 3.708099244 Solving -1.5 + t = 3.708099244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.708099244 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.708099244 + 1.5 t = 3.708099244 + 1.5 Combine like terms: 3.708099244 + 1.5 = 5.208099244 t = 5.208099244 Simplifying t = 5.208099244Subproblem 2
t + -1.5 = -3.708099244 Simplifying t + -1.5 = -3.708099244 Reorder the terms: -1.5 + t = -3.708099244 Solving -1.5 + t = -3.708099244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.708099244 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.708099244 + 1.5 t = -3.708099244 + 1.5 Combine like terms: -3.708099244 + 1.5 = -2.208099244 t = -2.208099244 Simplifying t = -2.208099244Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.208099244, -2.208099244}
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