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Simplifying -16t2 + -11t + 150 = 0 Reorder the terms: 150 + -11t + -16t2 = 0 Solving 150 + -11t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -9.375 + 0.6875t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 0.6875t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 0.6875t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 0.6875t + t2 = 0 + 9.375 0.6875t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 0.6875t + t2 = 9.375 The t term is 0.6875t. Take half its coefficient (0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. 0.6875t + 0.1181640625 + t2 = 9.375 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875t + t2 = 9.375 + 0.1181640625 Combine like terms: 9.375 + 0.1181640625 = 9.4931640625 0.1181640625 + 0.6875t + t2 = 9.4931640625 Factor a perfect square on the left side: (t + 0.34375)(t + 0.34375) = 9.4931640625 Calculate the square root of the right side: 3.081097866 Break this problem into two subproblems by setting (t + 0.34375) equal to 3.081097866 and -3.081097866.Subproblem 1
t + 0.34375 = 3.081097866 Simplifying t + 0.34375 = 3.081097866 Reorder the terms: 0.34375 + t = 3.081097866 Solving 0.34375 + t = 3.081097866 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + t = 3.081097866 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = 3.081097866 + -0.34375 t = 3.081097866 + -0.34375 Combine like terms: 3.081097866 + -0.34375 = 2.737347866 t = 2.737347866 Simplifying t = 2.737347866Subproblem 2
t + 0.34375 = -3.081097866 Simplifying t + 0.34375 = -3.081097866 Reorder the terms: 0.34375 + t = -3.081097866 Solving 0.34375 + t = -3.081097866 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + t = -3.081097866 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = -3.081097866 + -0.34375 t = -3.081097866 + -0.34375 Combine like terms: -3.081097866 + -0.34375 = -3.424847866 t = -3.424847866 Simplifying t = -3.424847866Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.737347866, -3.424847866}
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