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Simplifying 8t5 + 2t4 = -10t3 Reorder the terms: 2t4 + 8t5 = -10t3 Solving 2t4 + 8t5 = -10t3 Solving for variable 't'. Reorder the terms: 10t3 + 2t4 + 8t5 = -10t3 + 10t3 Combine like terms: -10t3 + 10t3 = 0 10t3 + 2t4 + 8t5 = 0 Factor out the Greatest Common Factor (GCF), '2t3'. 2t3(5 + t + 4t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't3' equal to zero and attempt to solve: Simplifying t3 = 0 Solving t3 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + t + 4t2)' equal to zero and attempt to solve: Simplifying 5 + t + 4t2 = 0 Solving 5 + t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.25t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.25t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.25t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.25t + t2 = 0 + -1.25 0.25t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.25t + t2 = -1.25 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25t + 0.25 + t2 = -1.25 + 0.25 Reorder the terms: 0.25 + 0.25t + t2 = -1.25 + 0.25 Combine like terms: -1.25 + 0.25 = -1 0.25 + 0.25t + t2 = -1 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -1 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. The solution to this equation could not be determined.
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