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Simplifying 2t2 = 36 + 12t Solving 2t2 = 36 + 12t Solving for variable 't'. Reorder the terms: -36 + -12t + 2t2 = 36 + 12t + -36 + -12t Reorder the terms: -36 + -12t + 2t2 = 36 + -36 + 12t + -12t Combine like terms: 36 + -36 = 0 -36 + -12t + 2t2 = 0 + 12t + -12t -36 + -12t + 2t2 = 12t + -12t Combine like terms: 12t + -12t = 0 -36 + -12t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -6t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -6t + t2)' equal to zero and attempt to solve: Simplifying -18 + -6t + t2 = 0 Solving -18 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6t + 18 + t2 = 0 + 18 Reorder the terms: -18 + 18 + -6t + t2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6t + t2 = 0 + 18 -6t + t2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6t + t2 = 18 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 18 + 9 Reorder the terms: 9 + -6t + t2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6t + t2 = 27 Factor a perfect square on the left side: (t + -3)(t + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (t + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
t + -3 = 5.196152423 Simplifying t + -3 = 5.196152423 Reorder the terms: -3 + t = 5.196152423 Solving -3 + t = 5.196152423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + t = 5.196152423 + 3 t = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 t = 8.196152423 Simplifying t = 8.196152423Subproblem 2
t + -3 = -5.196152423 Simplifying t + -3 = -5.196152423 Reorder the terms: -3 + t = -5.196152423 Solving -3 + t = -5.196152423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + t = -5.196152423 + 3 t = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 t = -2.196152423 Simplifying t = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.196152423, -2.196152423}Solution
t = {8.196152423, -2.196152423}
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