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Simplifying 4t2 + -24t + 48 = 0 Reorder the terms: 48 + -24t + 4t2 = 0 Solving 48 + -24t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + -6t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + -6t + t2)' equal to zero and attempt to solve: Simplifying 12 + -6t + t2 = 0 Solving 12 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -6t + -12 + t2 = 0 + -12 Reorder the terms: 12 + -12 + -6t + t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6t + t2 = 0 + -12 -6t + t2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6t + t2 = -12 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -12 + 9 Reorder the terms: 9 + -6t + t2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + -6t + t2 = -3 Factor a perfect square on the left side: (t + -3)(t + -3) = -3 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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