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Simplifying 40t3 + 25t2 + 80t = 0 Reorder the terms: 80t + 25t2 + 40t3 = 0 Solving 80t + 25t2 + 40t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5t'. 5t(16 + 5t + 8t2) = 0 Ignore the factor 5.Subproblem 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 '(16 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying 16 + 5t + 8t2 = 0 Solving 16 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2 + 0.625t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.625t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 0.625t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.625t + t2 = 0 + -2 0.625t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.625t + t2 = -2 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = -2 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = -2 + 0.09765625 Combine like terms: -2 + 0.09765625 = -1.90234375 0.09765625 + 0.625t + t2 = -1.90234375 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = -1.90234375 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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