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Simplifying -16t2 + 11t + 4 = 0 Reorder the terms: 4 + 11t + -16t2 = 0 Solving 4 + 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'. -0.25 + -0.6875t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.6875t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.6875t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.6875t + t2 = 0 + 0.25 -0.6875t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.6875t + t2 = 0.25 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 = 0.25 + 0.1181640625 Reorder the terms: 0.1181640625 + -0.6875t + t2 = 0.25 + 0.1181640625 Combine like terms: 0.25 + 0.1181640625 = 0.3681640625 0.1181640625 + -0.6875t + t2 = 0.3681640625 Factor a perfect square on the left side: (t + -0.34375)(t + -0.34375) = 0.3681640625 Calculate the square root of the right side: 0.606765245 Break this problem into two subproblems by setting (t + -0.34375) equal to 0.606765245 and -0.606765245.Subproblem 1
t + -0.34375 = 0.606765245 Simplifying t + -0.34375 = 0.606765245 Reorder the terms: -0.34375 + t = 0.606765245 Solving -0.34375 + t = 0.606765245 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 = 0.606765245 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + t = 0.606765245 + 0.34375 t = 0.606765245 + 0.34375 Combine like terms: 0.606765245 + 0.34375 = 0.950515245 t = 0.950515245 Simplifying t = 0.950515245Subproblem 2
t + -0.34375 = -0.606765245 Simplifying t + -0.34375 = -0.606765245 Reorder the terms: -0.34375 + t = -0.606765245 Solving -0.34375 + t = -0.606765245 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 = -0.606765245 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + t = -0.606765245 + 0.34375 t = -0.606765245 + 0.34375 Combine like terms: -0.606765245 + 0.34375 = -0.263015245 t = -0.263015245 Simplifying t = -0.263015245Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.950515245, -0.263015245}
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