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Simplifying 0 = -16t2 + 76t + 135 Reorder the terms: 0 = 135 + 76t + -16t2 Solving 0 = 135 + 76t + -16t2 Solving for variable 't'. Combine like terms: 0 + -135 = -135 -135 + -76t + 16t2 = 135 + 76t + -16t2 + -135 + -76t + 16t2 Reorder the terms: -135 + -76t + 16t2 = 135 + -135 + 76t + -76t + -16t2 + 16t2 Combine like terms: 135 + -135 = 0 -135 + -76t + 16t2 = 0 + 76t + -76t + -16t2 + 16t2 -135 + -76t + 16t2 = 76t + -76t + -16t2 + 16t2 Combine like terms: 76t + -76t = 0 -135 + -76t + 16t2 = 0 + -16t2 + 16t2 -135 + -76t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -135 + -76t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -8.4375 + -4.75t + t2 = 0 Move the constant term to the right: Add '8.4375' to each side of the equation. -8.4375 + -4.75t + 8.4375 + t2 = 0 + 8.4375 Reorder the terms: -8.4375 + 8.4375 + -4.75t + t2 = 0 + 8.4375 Combine like terms: -8.4375 + 8.4375 = 0.0000 0.0000 + -4.75t + t2 = 0 + 8.4375 -4.75t + t2 = 0 + 8.4375 Combine like terms: 0 + 8.4375 = 8.4375 -4.75t + t2 = 8.4375 The t term is -4.75t. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75t + 5.640625 + t2 = 8.4375 + 5.640625 Reorder the terms: 5.640625 + -4.75t + t2 = 8.4375 + 5.640625 Combine like terms: 8.4375 + 5.640625 = 14.078125 5.640625 + -4.75t + t2 = 14.078125 Factor a perfect square on the left side: (t + -2.375)(t + -2.375) = 14.078125 Calculate the square root of the right side: 3.752082755 Break this problem into two subproblems by setting (t + -2.375) equal to 3.752082755 and -3.752082755.Subproblem 1
t + -2.375 = 3.752082755 Simplifying t + -2.375 = 3.752082755 Reorder the terms: -2.375 + t = 3.752082755 Solving -2.375 + t = 3.752082755 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + t = 3.752082755 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + t = 3.752082755 + 2.375 t = 3.752082755 + 2.375 Combine like terms: 3.752082755 + 2.375 = 6.127082755 t = 6.127082755 Simplifying t = 6.127082755Subproblem 2
t + -2.375 = -3.752082755 Simplifying t + -2.375 = -3.752082755 Reorder the terms: -2.375 + t = -3.752082755 Solving -2.375 + t = -3.752082755 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + t = -3.752082755 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + t = -3.752082755 + 2.375 t = -3.752082755 + 2.375 Combine like terms: -3.752082755 + 2.375 = -1.377082755 t = -1.377082755 Simplifying t = -1.377082755Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.127082755, -1.377082755}
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