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Simplifying -16t2 + 8t = 80 Reorder the terms: 8t + -16t2 = 80 Solving 8t + -16t2 = 80 Solving for variable 't'. Reorder the terms: -80 + 8t + -16t2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 8t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-10 + t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-10 + t + -2t2)' equal to zero and attempt to solve: Simplifying -10 + t + -2t2 = 0 Solving -10 + t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5 + -0.5t + t2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -0.5t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -0.5t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -0.5t + t2 = 0 + -5 -0.5t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -0.5t + t2 = -5 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5t + 0.25 + t2 = -5 + 0.25 Reorder the terms: 0.25 + -0.5t + t2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + -0.5t + t2 = -4.75 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -4.75 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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