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Simplifying 32 = -16t2 + 44t + -4 Reorder the terms: 32 = -4 + 44t + -16t2 Solving 32 = -4 + 44t + -16t2 Solving for variable 't'. Combine like terms: 32 + 4 = 36 36 + -44t + 16t2 = -4 + 44t + -16t2 + 4 + -44t + 16t2 Reorder the terms: 36 + -44t + 16t2 = -4 + 4 + 44t + -44t + -16t2 + 16t2 Combine like terms: -4 + 4 = 0 36 + -44t + 16t2 = 0 + 44t + -44t + -16t2 + 16t2 36 + -44t + 16t2 = 44t + -44t + -16t2 + 16t2 Combine like terms: 44t + -44t = 0 36 + -44t + 16t2 = 0 + -16t2 + 16t2 36 + -44t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 36 + -44t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -11t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -11t + 4t2)' equal to zero and attempt to solve: Simplifying 9 + -11t + 4t2 = 0 Solving 9 + -11t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -2.75t + t2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -2.75t + -2.25 + t2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -2.75t + t2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -2.75t + t2 = 0 + -2.25 -2.75t + t2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -2.75t + t2 = -2.25 The t term is -2.75t. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75t + 1.890625 + t2 = -2.25 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = -2.25 + 1.890625 Combine like terms: -2.25 + 1.890625 = -0.359375 1.890625 + -2.75t + t2 = -0.359375 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = -0.359375 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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