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Simplifying 12288 = -16t2 + 32t + 384 Reorder the terms: 12288 = 384 + 32t + -16t2 Solving 12288 = 384 + 32t + -16t2 Solving for variable 't'. Combine like terms: 12288 + -384 = 11904 11904 + -32t + 16t2 = 384 + 32t + -16t2 + -384 + -32t + 16t2 Reorder the terms: 11904 + -32t + 16t2 = 384 + -384 + 32t + -32t + -16t2 + 16t2 Combine like terms: 384 + -384 = 0 11904 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 11904 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 11904 + -32t + 16t2 = 0 + -16t2 + 16t2 11904 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 11904 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(744 + -2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(744 + -2t + t2)' equal to zero and attempt to solve: Simplifying 744 + -2t + t2 = 0 Solving 744 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-744' to each side of the equation. 744 + -2t + -744 + t2 = 0 + -744 Reorder the terms: 744 + -744 + -2t + t2 = 0 + -744 Combine like terms: 744 + -744 = 0 0 + -2t + t2 = 0 + -744 -2t + t2 = 0 + -744 Combine like terms: 0 + -744 = -744 -2t + t2 = -744 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -744 + 1 Reorder the terms: 1 + -2t + t2 = -744 + 1 Combine like terms: -744 + 1 = -743 1 + -2t + t2 = -743 Factor a perfect square on the left side: (t + -1)(t + -1) = -743 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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