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Simplifying 0 = 16t2 + -48t + 64 Reorder the terms: 0 = 64 + -48t + 16t2 Solving 0 = 64 + -48t + 16t2 Solving for variable 't'. Combine like terms: 0 + -64 = -64 -64 + 48t + -16t2 = 64 + -48t + 16t2 + -64 + 48t + -16t2 Reorder the terms: -64 + 48t + -16t2 = 64 + -64 + -48t + 48t + 16t2 + -16t2 Combine like terms: 64 + -64 = 0 -64 + 48t + -16t2 = 0 + -48t + 48t + 16t2 + -16t2 -64 + 48t + -16t2 = -48t + 48t + 16t2 + -16t2 Combine like terms: -48t + 48t = 0 -64 + 48t + -16t2 = 0 + 16t2 + -16t2 -64 + 48t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -64 + 48t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-4 + 3t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-4 + 3t + -1t2)' equal to zero and attempt to solve: Simplifying -4 + 3t + -1t2 = 0 Solving -4 + 3t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -3t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -3t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t + t2 = 0 + -4 -3t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3t + t2 = -4 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 = -4 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3t + t2 = -1.75 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -1.75 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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