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Simplifying -8t2 + 7t + 9t3 + -1t3 + 10t2 + -4t = 0 Reorder the terms: 7t + -4t + -8t2 + 10t2 + 9t3 + -1t3 = 0 Combine like terms: 7t + -4t = 3t 3t + -8t2 + 10t2 + 9t3 + -1t3 = 0 Combine like terms: -8t2 + 10t2 = 2t2 3t + 2t2 + 9t3 + -1t3 = 0 Combine like terms: 9t3 + -1t3 = 8t3 3t + 2t2 + 8t3 = 0 Solving 3t + 2t2 + 8t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(3 + 2t + 8t2) = 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 '(3 + 2t + 8t2)' equal to zero and attempt to solve: Simplifying 3 + 2t + 8t2 = 0 Solving 3 + 2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 0.25t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 0.25t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 0.25t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 0.25t + t2 = 0 + -0.375 0.25t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 0.25t + t2 = -0.375 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = -0.375 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = -0.375 + 0.015625 Combine like terms: -0.375 + 0.015625 = -0.359375 0.015625 + 0.25t + t2 = -0.359375 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = -0.359375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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