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Simplifying 8t2 + 11t + -150 = 0 Reorder the terms: -150 + 11t + 8t2 = 0 Solving -150 + 11t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -18.75 + 1.375t + t2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 1.375t + 18.75 + t2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 1.375t + t2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 1.375t + t2 = 0 + 18.75 1.375t + t2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 1.375t + t2 = 18.75 The t term is 1.375t. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375t + 0.47265625 + t2 = 18.75 + 0.47265625 Reorder the terms: 0.47265625 + 1.375t + t2 = 18.75 + 0.47265625 Combine like terms: 18.75 + 0.47265625 = 19.22265625 0.47265625 + 1.375t + t2 = 19.22265625 Factor a perfect square on the left side: (t + 0.6875)(t + 0.6875) = 19.22265625 Calculate the square root of the right side: 4.384364977 Break this problem into two subproblems by setting (t + 0.6875) equal to 4.384364977 and -4.384364977.Subproblem 1
t + 0.6875 = 4.384364977 Simplifying t + 0.6875 = 4.384364977 Reorder the terms: 0.6875 + t = 4.384364977 Solving 0.6875 + t = 4.384364977 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + t = 4.384364977 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + t = 4.384364977 + -0.6875 t = 4.384364977 + -0.6875 Combine like terms: 4.384364977 + -0.6875 = 3.696864977 t = 3.696864977 Simplifying t = 3.696864977Subproblem 2
t + 0.6875 = -4.384364977 Simplifying t + 0.6875 = -4.384364977 Reorder the terms: 0.6875 + t = -4.384364977 Solving 0.6875 + t = -4.384364977 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + t = -4.384364977 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + t = -4.384364977 + -0.6875 t = -4.384364977 + -0.6875 Combine like terms: -4.384364977 + -0.6875 = -5.071864977 t = -5.071864977 Simplifying t = -5.071864977Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.696864977, -5.071864977}
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