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Simplifying 2t(t + 6) = 6 Reorder the terms: 2t(6 + t) = 6 (6 * 2t + t * 2t) = 6 (12t + 2t2) = 6 Solving 12t + 2t2 = 6 Solving for variable 't'. Reorder the terms: -6 + 12t + 2t2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 12t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 6t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 6t + t2)' equal to zero and attempt to solve: Simplifying -3 + 6t + t2 = 0 Solving -3 + 6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 6t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6t + t2 = 0 + 3 6t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 6t + t2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6t + t2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6t + t2 = 12 Factor a perfect square on the left side: (t + 3)(t + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
t + 3 = 3.464101615 Simplifying t + 3 = 3.464101615 Reorder the terms: 3 + t = 3.464101615 Solving 3 + t = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.464101615 + -3 t = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 t = 0.464101615 Simplifying t = 0.464101615Subproblem 2
t + 3 = -3.464101615 Simplifying t + 3 = -3.464101615 Reorder the terms: 3 + t = -3.464101615 Solving 3 + t = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.464101615 + -3 t = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 t = -6.464101615 Simplifying t = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.464101615, -6.464101615}Solution
t = {0.464101615, -6.464101615}
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