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Simplifying 80t2 + -44t + 180 = 0 Reorder the terms: 180 + -44t + 80t2 = 0 Solving 180 + -44t + 80t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(45 + -11t + 20t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(45 + -11t + 20t2)' equal to zero and attempt to solve: Simplifying 45 + -11t + 20t2 = 0 Solving 45 + -11t + 20t2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 2.25 + -0.55t + t2 = 0.0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -0.55t + -2.25 + t2 = 0.0 + -2.25 Reorder the terms: 2.25 + -2.25 + -0.55t + t2 = 0.0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -0.55t + t2 = 0.0 + -2.25 -0.55t + t2 = 0.0 + -2.25 Combine like terms: 0.0 + -2.25 = -2.25 -0.55t + t2 = -2.25 The t term is -0.55t. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55t + 0.075625 + t2 = -2.25 + 0.075625 Reorder the terms: 0.075625 + -0.55t + t2 = -2.25 + 0.075625 Combine like terms: -2.25 + 0.075625 = -2.174375 0.075625 + -0.55t + t2 = -2.174375 Factor a perfect square on the left side: (t + -0.275)(t + -0.275) = -2.174375 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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