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Simplifying 130 = -16t2 + 80t + 20 Reorder the terms: 130 = 20 + 80t + -16t2 Solving 130 = 20 + 80t + -16t2 Solving for variable 't'. Combine like terms: 130 + -20 = 110 110 + -80t + 16t2 = 20 + 80t + -16t2 + -20 + -80t + 16t2 Reorder the terms: 110 + -80t + 16t2 = 20 + -20 + 80t + -80t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 110 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 110 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 110 + -80t + 16t2 = 0 + -16t2 + 16t2 110 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 110 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -40t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -40t + 8t2)' equal to zero and attempt to solve: Simplifying 55 + -40t + 8t2 = 0 Solving 55 + -40t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.875 + -5t + t2 = 0 Move the constant term to the right: Add '-6.875' to each side of the equation. 6.875 + -5t + -6.875 + t2 = 0 + -6.875 Reorder the terms: 6.875 + -6.875 + -5t + t2 = 0 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + -5t + t2 = 0 + -6.875 -5t + t2 = 0 + -6.875 Combine like terms: 0 + -6.875 = -6.875 -5t + t2 = -6.875 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -6.875 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -6.875 + 6.25 Combine like terms: -6.875 + 6.25 = -0.625 6.25 + -5t + t2 = -0.625 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -0.625 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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