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Simplifying -16t2 + 46t + 9 = 0 Reorder the terms: 9 + 46t + -16t2 = 0 Solving 9 + 46t + -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'. -0.5625 + -2.875t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -2.875t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -2.875t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -2.875t + t2 = 0 + 0.5625 -2.875t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -2.875t + t2 = 0.5625 The t term is -2.875t. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875t + 2.06640625 + t2 = 0.5625 + 2.06640625 Reorder the terms: 2.06640625 + -2.875t + t2 = 0.5625 + 2.06640625 Combine like terms: 0.5625 + 2.06640625 = 2.62890625 2.06640625 + -2.875t + t2 = 2.62890625 Factor a perfect square on the left side: (t + -1.4375)(t + -1.4375) = 2.62890625 Calculate the square root of the right side: 1.621390221 Break this problem into two subproblems by setting (t + -1.4375) equal to 1.621390221 and -1.621390221.Subproblem 1
t + -1.4375 = 1.621390221 Simplifying t + -1.4375 = 1.621390221 Reorder the terms: -1.4375 + t = 1.621390221 Solving -1.4375 + t = 1.621390221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = 1.621390221 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = 1.621390221 + 1.4375 t = 1.621390221 + 1.4375 Combine like terms: 1.621390221 + 1.4375 = 3.058890221 t = 3.058890221 Simplifying t = 3.058890221Subproblem 2
t + -1.4375 = -1.621390221 Simplifying t + -1.4375 = -1.621390221 Reorder the terms: -1.4375 + t = -1.621390221 Solving -1.4375 + t = -1.621390221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = -1.621390221 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = -1.621390221 + 1.4375 t = -1.621390221 + 1.4375 Combine like terms: -1.621390221 + 1.4375 = -0.183890221 t = -0.183890221 Simplifying t = -0.183890221Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.058890221, -0.183890221}
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