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Simplifying -1t2 + -12t + -24 = 0 Reorder the terms: -24 + -12t + -1t2 = 0 Solving -24 + -12t + -1t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 12t + t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 12t + t2)' equal to zero and attempt to solve: Simplifying 24 + 12t + t2 = 0 Solving 24 + 12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 12t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + 12t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12t + t2 = 0 + -24 12t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 12t + t2 = -24 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = -24 + 36 Reorder the terms: 36 + 12t + t2 = -24 + 36 Combine like terms: -24 + 36 = 12 36 + 12t + t2 = 12 Factor a perfect square on the left side: (t + 6)(t + 6) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + 6) equal to 3.464101615 and -3.464101615.Subproblem 1
t + 6 = 3.464101615 Simplifying t + 6 = 3.464101615 Reorder the terms: 6 + t = 3.464101615 Solving 6 + t = 3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + t = 3.464101615 + -6 t = 3.464101615 + -6 Combine like terms: 3.464101615 + -6 = -2.535898385 t = -2.535898385 Simplifying t = -2.535898385Subproblem 2
t + 6 = -3.464101615 Simplifying t + 6 = -3.464101615 Reorder the terms: 6 + t = -3.464101615 Solving 6 + t = -3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + t = -3.464101615 + -6 t = -3.464101615 + -6 Combine like terms: -3.464101615 + -6 = -9.464101615 t = -9.464101615 Simplifying t = -9.464101615Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.535898385, -9.464101615}Solution
t = {-2.535898385, -9.464101615}
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