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Simplifying 5184(t) = -16t2 + 5184 Reorder the terms: 5184t = 5184 + -16t2 Solving 5184t = 5184 + -16t2 Solving for variable 't'. Reorder the terms: -5184 + 5184t + 16t2 = 5184 + -16t2 + -5184 + 16t2 Reorder the terms: -5184 + 5184t + 16t2 = 5184 + -5184 + -16t2 + 16t2 Combine like terms: 5184 + -5184 = 0 -5184 + 5184t + 16t2 = 0 + -16t2 + 16t2 -5184 + 5184t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5184 + 5184t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-324 + 324t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-324 + 324t + t2)' equal to zero and attempt to solve: Simplifying -324 + 324t + t2 = 0 Solving -324 + 324t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 324t + 324 + t2 = 0 + 324 Reorder the terms: -324 + 324 + 324t + t2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 324t + t2 = 0 + 324 324t + t2 = 0 + 324 Combine like terms: 0 + 324 = 324 324t + t2 = 324 The t term is 324t. Take half its coefficient (162). Square it (26244) and add it to both sides. Add '26244' to each side of the equation. 324t + 26244 + t2 = 324 + 26244 Reorder the terms: 26244 + 324t + t2 = 324 + 26244 Combine like terms: 324 + 26244 = 26568 26244 + 324t + t2 = 26568 Factor a perfect square on the left side: (t + 162)(t + 162) = 26568 Calculate the square root of the right side: 162.996932486 Break this problem into two subproblems by setting (t + 162) equal to 162.996932486 and -162.996932486.Subproblem 1
t + 162 = 162.996932486 Simplifying t + 162 = 162.996932486 Reorder the terms: 162 + t = 162.996932486 Solving 162 + t = 162.996932486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-162' to each side of the equation. 162 + -162 + t = 162.996932486 + -162 Combine like terms: 162 + -162 = 0 0 + t = 162.996932486 + -162 t = 162.996932486 + -162 Combine like terms: 162.996932486 + -162 = 0.996932486 t = 0.996932486 Simplifying t = 0.996932486Subproblem 2
t + 162 = -162.996932486 Simplifying t + 162 = -162.996932486 Reorder the terms: 162 + t = -162.996932486 Solving 162 + t = -162.996932486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-162' to each side of the equation. 162 + -162 + t = -162.996932486 + -162 Combine like terms: 162 + -162 = 0 0 + t = -162.996932486 + -162 t = -162.996932486 + -162 Combine like terms: -162.996932486 + -162 = -324.996932486 t = -324.996932486 Simplifying t = -324.996932486Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.996932486, -324.996932486}Solution
t = {0.996932486, -324.996932486}
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