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Simplifying -16t2 + 138t + 55 = 0 Reorder the terms: 55 + 138t + -16t2 = 0 Solving 55 + 138t + -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'. -3.4375 + -8.625t + t2 = 0 Move the constant term to the right: Add '3.4375' to each side of the equation. -3.4375 + -8.625t + 3.4375 + t2 = 0 + 3.4375 Reorder the terms: -3.4375 + 3.4375 + -8.625t + t2 = 0 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + -8.625t + t2 = 0 + 3.4375 -8.625t + t2 = 0 + 3.4375 Combine like terms: 0 + 3.4375 = 3.4375 -8.625t + t2 = 3.4375 The t term is -8.625t. Take half its coefficient (-4.3125). Square it (18.59765625) and add it to both sides. Add '18.59765625' to each side of the equation. -8.625t + 18.59765625 + t2 = 3.4375 + 18.59765625 Reorder the terms: 18.59765625 + -8.625t + t2 = 3.4375 + 18.59765625 Combine like terms: 3.4375 + 18.59765625 = 22.03515625 18.59765625 + -8.625t + t2 = 22.03515625 Factor a perfect square on the left side: (t + -4.3125)(t + -4.3125) = 22.03515625 Calculate the square root of the right side: 4.694161933 Break this problem into two subproblems by setting (t + -4.3125) equal to 4.694161933 and -4.694161933.Subproblem 1
t + -4.3125 = 4.694161933 Simplifying t + -4.3125 = 4.694161933 Reorder the terms: -4.3125 + t = 4.694161933 Solving -4.3125 + t = 4.694161933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.3125' to each side of the equation. -4.3125 + 4.3125 + t = 4.694161933 + 4.3125 Combine like terms: -4.3125 + 4.3125 = 0.0000 0.0000 + t = 4.694161933 + 4.3125 t = 4.694161933 + 4.3125 Combine like terms: 4.694161933 + 4.3125 = 9.006661933 t = 9.006661933 Simplifying t = 9.006661933Subproblem 2
t + -4.3125 = -4.694161933 Simplifying t + -4.3125 = -4.694161933 Reorder the terms: -4.3125 + t = -4.694161933 Solving -4.3125 + t = -4.694161933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.3125' to each side of the equation. -4.3125 + 4.3125 + t = -4.694161933 + 4.3125 Combine like terms: -4.3125 + 4.3125 = 0.0000 0.0000 + t = -4.694161933 + 4.3125 t = -4.694161933 + 4.3125 Combine like terms: -4.694161933 + 4.3125 = -0.381661933 t = -0.381661933 Simplifying t = -0.381661933Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.006661933, -0.381661933}
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