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Simplifying t3 + 8t2 + 4t = 0 Reorder the terms: 4t + 8t2 + t3 = 0 Solving 4t + 8t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(4 + 8t + t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(4 + 8t + t2)' equal to zero and attempt to solve: Simplifying 4 + 8t + t2 = 0 Solving 4 + 8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 8t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + 8t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8t + t2 = 0 + -4 8t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 8t + t2 = -4 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = -4 + 16 Reorder the terms: 16 + 8t + t2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + 8t + t2 = 12 Factor a perfect square on the left side: (t + 4)(t + 4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + 4) equal to 3.464101615 and -3.464101615.Subproblem 1
t + 4 = 3.464101615 Simplifying t + 4 = 3.464101615 Reorder the terms: 4 + t = 3.464101615 Solving 4 + t = 3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + t = 3.464101615 + -4 t = 3.464101615 + -4 Combine like terms: 3.464101615 + -4 = -0.535898385 t = -0.535898385 Simplifying t = -0.535898385Subproblem 2
t + 4 = -3.464101615 Simplifying t + 4 = -3.464101615 Reorder the terms: 4 + t = -3.464101615 Solving 4 + t = -3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + t = -3.464101615 + -4 t = -3.464101615 + -4 Combine like terms: -3.464101615 + -4 = -7.464101615 t = -7.464101615 Simplifying t = -7.464101615Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.535898385, -7.464101615}Solution
t = {0, -0.535898385, -7.464101615}
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