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Simplifying 3t9(t + -1t2 + 4t3) = 0 (t * 3t9 + -1t2 * 3t9 + 4t3 * 3t9) = 0 (3t10 + -3t11 + 12t12) = 0 Solving 3t10 + -3t11 + 12t12 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t10'. 3t10(1 + -1t + 4t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 't10' equal to zero and attempt to solve: Simplifying t10 = 0 Solving t10 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t10 = 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 '(1 + -1t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + -1t + 4t2 = 0 Solving 1 + -1t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -0.25t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.25t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.25t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.25t + t2 = 0 + -0.25 -0.25t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.25t + t2 = -0.25 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 = -0.25 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = -0.25 + 0.015625 Combine like terms: -0.25 + 0.015625 = -0.234375 0.015625 + -0.25t + t2 = -0.234375 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = -0.234375 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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