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Simplifying 48 = -16t2 + 48t + 4 Reorder the terms: 48 = 4 + 48t + -16t2 Solving 48 = 4 + 48t + -16t2 Solving for variable 't'. Combine like terms: 48 + -4 = 44 44 + -48t + 16t2 = 4 + 48t + -16t2 + -4 + -48t + 16t2 Reorder the terms: 44 + -48t + 16t2 = 4 + -4 + 48t + -48t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 44 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 44 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 44 + -48t + 16t2 = 0 + -16t2 + 16t2 44 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 44 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -12t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -12t + 4t2)' equal to zero and attempt to solve: Simplifying 11 + -12t + 4t2 = 0 Solving 11 + -12t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -3t + t2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -3t + -2.75 + t2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -3t + t2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -3t + t2 = 0 + -2.75 -3t + t2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -3t + t2 = -2.75 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = -2.75 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -2.75 + 2.25 Combine like terms: -2.75 + 2.25 = -0.5 2.25 + -3t + t2 = -0.5 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -0.5 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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