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Simplifying 0 = -16t2 + 44t + 200 Reorder the terms: 0 = 200 + 44t + -16t2 Solving 0 = 200 + 44t + -16t2 Solving for variable 't'. Combine like terms: 0 + -200 = -200 -200 + -44t + 16t2 = 200 + 44t + -16t2 + -200 + -44t + 16t2 Reorder the terms: -200 + -44t + 16t2 = 200 + -200 + 44t + -44t + -16t2 + 16t2 Combine like terms: 200 + -200 = 0 -200 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 -200 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 -200 + -44t + 16t2 = 0 + -16t2 + 16t2 -200 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -200 + -44t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + -11t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + -11t + 4t2)' equal to zero and attempt to solve: Simplifying -50 + -11t + 4t2 = 0 Solving -50 + -11t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -2.75t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -2.75t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -2.75t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -2.75t + t2 = 0 + 12.5 -2.75t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -2.75t + t2 = 12.5 The t term is -2.75t. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75t + 1.890625 + t2 = 12.5 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = 12.5 + 1.890625 Combine like terms: 12.5 + 1.890625 = 14.390625 1.890625 + -2.75t + t2 = 14.390625 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = 14.390625 Calculate the square root of the right side: 3.793497726 Break this problem into two subproblems by setting (t + -1.375) equal to 3.793497726 and -3.793497726.Subproblem 1
t + -1.375 = 3.793497726 Simplifying t + -1.375 = 3.793497726 Reorder the terms: -1.375 + t = 3.793497726 Solving -1.375 + t = 3.793497726 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = 3.793497726 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = 3.793497726 + 1.375 t = 3.793497726 + 1.375 Combine like terms: 3.793497726 + 1.375 = 5.168497726 t = 5.168497726 Simplifying t = 5.168497726Subproblem 2
t + -1.375 = -3.793497726 Simplifying t + -1.375 = -3.793497726 Reorder the terms: -1.375 + t = -3.793497726 Solving -1.375 + t = -3.793497726 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + t = -3.793497726 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + t = -3.793497726 + 1.375 t = -3.793497726 + 1.375 Combine like terms: -3.793497726 + 1.375 = -2.418497726 t = -2.418497726 Simplifying t = -2.418497726Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.168497726, -2.418497726}Solution
t = {5.168497726, -2.418497726}
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