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Simplifying 4t3 + 3t2 + -36t = 0 Reorder the terms: -36t + 3t2 + 4t3 = 0 Solving -36t + 3t2 + 4t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-36 + 3t + 4t2) = 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 '(-36 + 3t + 4t2)' equal to zero and attempt to solve: Simplifying -36 + 3t + 4t2 = 0 Solving -36 + 3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9 + 0.75t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.75t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 0.75t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.75t + t2 = 0 + 9 0.75t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.75t + t2 = 9 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = 9 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 9 + 0.140625 Combine like terms: 9 + 0.140625 = 9.140625 0.140625 + 0.75t + t2 = 9.140625 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 9.140625 Calculate the square root of the right side: 3.023346656 Break this problem into two subproblems by setting (t + 0.375) equal to 3.023346656 and -3.023346656.Subproblem 1
t + 0.375 = 3.023346656 Simplifying t + 0.375 = 3.023346656 Reorder the terms: 0.375 + t = 3.023346656 Solving 0.375 + t = 3.023346656 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = 3.023346656 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 3.023346656 + -0.375 t = 3.023346656 + -0.375 Combine like terms: 3.023346656 + -0.375 = 2.648346656 t = 2.648346656 Simplifying t = 2.648346656Subproblem 2
t + 0.375 = -3.023346656 Simplifying t + 0.375 = -3.023346656 Reorder the terms: 0.375 + t = -3.023346656 Solving 0.375 + t = -3.023346656 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = -3.023346656 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -3.023346656 + -0.375 t = -3.023346656 + -0.375 Combine like terms: -3.023346656 + -0.375 = -3.398346656 t = -3.398346656 Simplifying t = -3.398346656Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.648346656, -3.398346656}Solution
t = {0, 2.648346656, -3.398346656}
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