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Simplifying 1122 = -16t2 + 48t + 64 Reorder the terms: 1122 = 64 + 48t + -16t2 Solving 1122 = 64 + 48t + -16t2 Solving for variable 't'. Combine like terms: 1122 + -64 = 1058 1058 + -48t + 16t2 = 64 + 48t + -16t2 + -64 + -48t + 16t2 Reorder the terms: 1058 + -48t + 16t2 = 64 + -64 + 48t + -48t + -16t2 + 16t2 Combine like terms: 64 + -64 = 0 1058 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 1058 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 1058 + -48t + 16t2 = 0 + -16t2 + 16t2 1058 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1058 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(529 + -24t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(529 + -24t + 8t2)' equal to zero and attempt to solve: Simplifying 529 + -24t + 8t2 = 0 Solving 529 + -24t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 66.125 + -3t + t2 = 0 Move the constant term to the right: Add '-66.125' to each side of the equation. 66.125 + -3t + -66.125 + t2 = 0 + -66.125 Reorder the terms: 66.125 + -66.125 + -3t + t2 = 0 + -66.125 Combine like terms: 66.125 + -66.125 = 0.000 0.000 + -3t + t2 = 0 + -66.125 -3t + t2 = 0 + -66.125 Combine like terms: 0 + -66.125 = -66.125 -3t + t2 = -66.125 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 = -66.125 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -66.125 + 2.25 Combine like terms: -66.125 + 2.25 = -63.875 2.25 + -3t + t2 = -63.875 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = -63.875 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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