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Simplifying 12t2 + 5t4 + -12t3 = 0 Reorder the terms: 12t2 + -12t3 + 5t4 = 0 Solving 12t2 + -12t3 + 5t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(12 + -12t + 5t2) = 0Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(12 + -12t + 5t2)' equal to zero and attempt to solve: Simplifying 12 + -12t + 5t2 = 0 Solving 12 + -12t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -2.4t + t2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -2.4t + -2.4 + t2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -2.4t + t2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -2.4t + t2 = 0 + -2.4 -2.4t + t2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -2.4t + t2 = -2.4 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = -2.4 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = -2.4 + 1.44 Combine like terms: -2.4 + 1.44 = -0.96 1.44 + -2.4t + t2 = -0.96 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = -0.96 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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