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Simplifying 0 = 8(2t2 + 9t + 56) Reorder the terms: 0 = 8(56 + 9t + 2t2) 0 = (56 * 8 + 9t * 8 + 2t2 * 8) 0 = (448 + 72t + 16t2) Solving 0 = 448 + 72t + 16t2 Solving for variable 't'. Combine like terms: 0 + -448 = -448 -448 + -72t + -16t2 = 448 + 72t + 16t2 + -448 + -72t + -16t2 Reorder the terms: -448 + -72t + -16t2 = 448 + -448 + 72t + -72t + 16t2 + -16t2 Combine like terms: 448 + -448 = 0 -448 + -72t + -16t2 = 0 + 72t + -72t + 16t2 + -16t2 -448 + -72t + -16t2 = 72t + -72t + 16t2 + -16t2 Combine like terms: 72t + -72t = 0 -448 + -72t + -16t2 = 0 + 16t2 + -16t2 -448 + -72t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -448 + -72t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-8'. -8(56 + 9t + 2t2) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(56 + 9t + 2t2)' equal to zero and attempt to solve: Simplifying 56 + 9t + 2t2 = 0 Solving 56 + 9t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 28 + 4.5t + t2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + 4.5t + -28 + t2 = 0 + -28 Reorder the terms: 28 + -28 + 4.5t + t2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 4.5t + t2 = 0 + -28 4.5t + t2 = 0 + -28 Combine like terms: 0 + -28 = -28 4.5t + t2 = -28 The t term is 4.5t. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5t + 5.0625 + t2 = -28 + 5.0625 Reorder the terms: 5.0625 + 4.5t + t2 = -28 + 5.0625 Combine like terms: -28 + 5.0625 = -22.9375 5.0625 + 4.5t + t2 = -22.9375 Factor a perfect square on the left side: (t + 2.25)(t + 2.25) = -22.9375 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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