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Simplifying 0 = -16t2 + -52t + 52 Reorder the terms: 0 = 52 + -52t + -16t2 Solving 0 = 52 + -52t + -16t2 Solving for variable 't'. Combine like terms: 0 + -52 = -52 -52 + 52t + 16t2 = 52 + -52t + -16t2 + -52 + 52t + 16t2 Reorder the terms: -52 + 52t + 16t2 = 52 + -52 + -52t + 52t + -16t2 + 16t2 Combine like terms: 52 + -52 = 0 -52 + 52t + 16t2 = 0 + -52t + 52t + -16t2 + 16t2 -52 + 52t + 16t2 = -52t + 52t + -16t2 + 16t2 Combine like terms: -52t + 52t = 0 -52 + 52t + 16t2 = 0 + -16t2 + 16t2 -52 + 52t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -52 + 52t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + 13t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + 13t + 4t2)' equal to zero and attempt to solve: Simplifying -13 + 13t + 4t2 = 0 Solving -13 + 13t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 3.25t + t2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 3.25t + 3.25 + t2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 3.25t + t2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 3.25t + t2 = 0 + 3.25 3.25t + t2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 3.25t + t2 = 3.25 The t term is 3.25t. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25t + 2.640625 + t2 = 3.25 + 2.640625 Reorder the terms: 2.640625 + 3.25t + t2 = 3.25 + 2.640625 Combine like terms: 3.25 + 2.640625 = 5.890625 2.640625 + 3.25t + t2 = 5.890625 Factor a perfect square on the left side: (t + 1.625)(t + 1.625) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (t + 1.625) equal to 2.42706098 and -2.42706098.Subproblem 1
t + 1.625 = 2.42706098 Simplifying t + 1.625 = 2.42706098 Reorder the terms: 1.625 + t = 2.42706098 Solving 1.625 + t = 2.42706098 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + t = 2.42706098 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + t = 2.42706098 + -1.625 t = 2.42706098 + -1.625 Combine like terms: 2.42706098 + -1.625 = 0.80206098 t = 0.80206098 Simplifying t = 0.80206098Subproblem 2
t + 1.625 = -2.42706098 Simplifying t + 1.625 = -2.42706098 Reorder the terms: 1.625 + t = -2.42706098 Solving 1.625 + t = -2.42706098 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + t = -2.42706098 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + t = -2.42706098 + -1.625 t = -2.42706098 + -1.625 Combine like terms: -2.42706098 + -1.625 = -4.05206098 t = -4.05206098 Simplifying t = -4.05206098Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.80206098, -4.05206098}Solution
t = {0.80206098, -4.05206098}
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