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Simplifying 277.5 + -2.5t = 555 + -16t2 Solving 277.5 + -2.5t = 555 + -16t2 Solving for variable 't'. Reorder the terms: 277.5 + -555 + -2.5t + 16t2 = 555 + -16t2 + -555 + 16t2 Combine like terms: 277.5 + -555 = -277.5 -277.5 + -2.5t + 16t2 = 555 + -16t2 + -555 + 16t2 Reorder the terms: -277.5 + -2.5t + 16t2 = 555 + -555 + -16t2 + 16t2 Combine like terms: 555 + -555 = 0 -277.5 + -2.5t + 16t2 = 0 + -16t2 + 16t2 -277.5 + -2.5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -277.5 + -2.5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -17.34375 + -0.15625t + t2 = 0 Move the constant term to the right: Add '17.34375' to each side of the equation. -17.34375 + -0.15625t + 17.34375 + t2 = 0 + 17.34375 Reorder the terms: -17.34375 + 17.34375 + -0.15625t + t2 = 0 + 17.34375 Combine like terms: -17.34375 + 17.34375 = 0.00000 0.00000 + -0.15625t + t2 = 0 + 17.34375 -0.15625t + t2 = 0 + 17.34375 Combine like terms: 0 + 17.34375 = 17.34375 -0.15625t + t2 = 17.34375 The t term is -0.15625t. Take half its coefficient (-0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. -0.15625t + 0.006103515625 + t2 = 17.34375 + 0.006103515625 Reorder the terms: 0.006103515625 + -0.15625t + t2 = 17.34375 + 0.006103515625 Combine like terms: 17.34375 + 0.006103515625 = 17.349853515625 0.006103515625 + -0.15625t + t2 = 17.349853515625 Factor a perfect square on the left side: (t + -0.078125)(t + -0.078125) = 17.349853515625 Calculate the square root of the right side: 4.165315536 Break this problem into two subproblems by setting (t + -0.078125) equal to 4.165315536 and -4.165315536.Subproblem 1
t + -0.078125 = 4.165315536 Simplifying t + -0.078125 = 4.165315536 Reorder the terms: -0.078125 + t = 4.165315536 Solving -0.078125 + t = 4.165315536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + t = 4.165315536 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + t = 4.165315536 + 0.078125 t = 4.165315536 + 0.078125 Combine like terms: 4.165315536 + 0.078125 = 4.243440536 t = 4.243440536 Simplifying t = 4.243440536Subproblem 2
t + -0.078125 = -4.165315536 Simplifying t + -0.078125 = -4.165315536 Reorder the terms: -0.078125 + t = -4.165315536 Solving -0.078125 + t = -4.165315536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + t = -4.165315536 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + t = -4.165315536 + 0.078125 t = -4.165315536 + 0.078125 Combine like terms: -4.165315536 + 0.078125 = -4.087190536 t = -4.087190536 Simplifying t = -4.087190536Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.243440536, -4.087190536}
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