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Simplifying 2t2 + -14t + 0 = 3 Reorder the terms: 0 + -14t + 2t2 = 3 Remove the zero: -14t + 2t2 = 3 Solving -14t + 2t2 = 3 Solving for variable 't'. Reorder the terms: -3 + -14t + 2t2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -14t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -7t + t2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -7t + 1.5 + t2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -7t + t2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -7t + t2 = 0 + 1.5 -7t + t2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -7t + t2 = 1.5 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 = 1.5 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 1.5 + 12.25 Combine like terms: 1.5 + 12.25 = 13.75 12.25 + -7t + t2 = 13.75 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (t + -3.5) equal to 3.708099244 and -3.708099244.Subproblem 1
t + -3.5 = 3.708099244 Simplifying t + -3.5 = 3.708099244 Reorder the terms: -3.5 + t = 3.708099244 Solving -3.5 + t = 3.708099244 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 = 3.708099244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.708099244 + 3.5 t = 3.708099244 + 3.5 Combine like terms: 3.708099244 + 3.5 = 7.208099244 t = 7.208099244 Simplifying t = 7.208099244Subproblem 2
t + -3.5 = -3.708099244 Simplifying t + -3.5 = -3.708099244 Reorder the terms: -3.5 + t = -3.708099244 Solving -3.5 + t = -3.708099244 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 = -3.708099244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.708099244 + 3.5 t = -3.708099244 + 3.5 Combine like terms: -3.708099244 + 3.5 = -0.208099244 t = -0.208099244 Simplifying t = -0.208099244Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.208099244, -0.208099244}
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