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Simplifying 6t2 + -12t + 54 = 0 Reorder the terms: 54 + -12t + 6t2 = 0 Solving 54 + -12t + 6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '6'. 6(9 + -2t + t2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(9 + -2t + t2)' equal to zero and attempt to solve: Simplifying 9 + -2t + t2 = 0 Solving 9 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -2t + -9 + t2 = 0 + -9 Reorder the terms: 9 + -9 + -2t + t2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2t + t2 = 0 + -9 -2t + t2 = 0 + -9 Combine like terms: 0 + -9 = -9 -2t + t2 = -9 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -9 + 1 Reorder the terms: 1 + -2t + t2 = -9 + 1 Combine like terms: -9 + 1 = -8 1 + -2t + t2 = -8 Factor a perfect square on the left side: (t + -1)(t + -1) = -8 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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