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Simplifying 0 = -16t2 + 1200t + 12389 Reorder the terms: 0 = 12389 + 1200t + -16t2 Solving 0 = 12389 + 1200t + -16t2 Solving for variable 't'. Combine like terms: 0 + -12389 = -12389 -12389 + -1200t + 16t2 = 12389 + 1200t + -16t2 + -12389 + -1200t + 16t2 Reorder the terms: -12389 + -1200t + 16t2 = 12389 + -12389 + 1200t + -1200t + -16t2 + 16t2 Combine like terms: 12389 + -12389 = 0 -12389 + -1200t + 16t2 = 0 + 1200t + -1200t + -16t2 + 16t2 -12389 + -1200t + 16t2 = 1200t + -1200t + -16t2 + 16t2 Combine like terms: 1200t + -1200t = 0 -12389 + -1200t + 16t2 = 0 + -16t2 + 16t2 -12389 + -1200t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12389 + -1200t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -774.3125 + -75t + t2 = 0 Move the constant term to the right: Add '774.3125' to each side of the equation. -774.3125 + -75t + 774.3125 + t2 = 0 + 774.3125 Reorder the terms: -774.3125 + 774.3125 + -75t + t2 = 0 + 774.3125 Combine like terms: -774.3125 + 774.3125 = 0.0000 0.0000 + -75t + t2 = 0 + 774.3125 -75t + t2 = 0 + 774.3125 Combine like terms: 0 + 774.3125 = 774.3125 -75t + t2 = 774.3125 The t term is -75t. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75t + 1406.25 + t2 = 774.3125 + 1406.25 Reorder the terms: 1406.25 + -75t + t2 = 774.3125 + 1406.25 Combine like terms: 774.3125 + 1406.25 = 2180.5625 1406.25 + -75t + t2 = 2180.5625 Factor a perfect square on the left side: (t + -37.5)(t + -37.5) = 2180.5625 Calculate the square root of the right side: 46.696493444 Break this problem into two subproblems by setting (t + -37.5) equal to 46.696493444 and -46.696493444.Subproblem 1
t + -37.5 = 46.696493444 Simplifying t + -37.5 = 46.696493444 Reorder the terms: -37.5 + t = 46.696493444 Solving -37.5 + t = 46.696493444 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + t = 46.696493444 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + t = 46.696493444 + 37.5 t = 46.696493444 + 37.5 Combine like terms: 46.696493444 + 37.5 = 84.196493444 t = 84.196493444 Simplifying t = 84.196493444Subproblem 2
t + -37.5 = -46.696493444 Simplifying t + -37.5 = -46.696493444 Reorder the terms: -37.5 + t = -46.696493444 Solving -37.5 + t = -46.696493444 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + t = -46.696493444 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + t = -46.696493444 + 37.5 t = -46.696493444 + 37.5 Combine like terms: -46.696493444 + 37.5 = -9.196493444 t = -9.196493444 Simplifying t = -9.196493444Solution
The solution to the problem is based on the solutions from the subproblems. t = {84.196493444, -9.196493444}
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