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Simplifying 56 = -16t2 + 56t Reorder the terms: 56 = 56t + -16t2 Solving 56 = 56t + -16t2 Solving for variable 't'. Reorder the terms: 56 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2 Combine like terms: 56t + -56t = 0 56 + -56t + 16t2 = 0 + -16t2 + 16t2 56 + -56t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 56 + -56t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(7 + -7t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(7 + -7t + 2t2)' equal to zero and attempt to solve: Simplifying 7 + -7t + 2t2 = 0 Solving 7 + -7t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -3.5t + t2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -3.5t + -3.5 + t2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -3.5t + t2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -3.5t + t2 = 0 + -3.5 -3.5t + t2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -3.5t + t2 = -3.5 The t term is -3.5t. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5t + 3.0625 + t2 = -3.5 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = -3.5 + 3.0625 Combine like terms: -3.5 + 3.0625 = -0.4375 3.0625 + -3.5t + t2 = -0.4375 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = -0.4375 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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