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Simplifying -2t2 + -14t + 3 = 0 Reorder the terms: 3 + -14t + -2t2 = 0 Solving 3 + -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'. -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 = 0.208099244 t = 0.208099244 Simplifying t = 0.208099244Subproblem 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 = -7.208099244 t = -7.208099244 Simplifying t = -7.208099244Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.208099244, -7.208099244}
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