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Simplifying -16t2 + 64t = 382 Reorder the terms: 64t + -16t2 = 382 Solving 64t + -16t2 = 382 Solving for variable 't'. Reorder the terms: -382 + 64t + -16t2 = 382 + -382 Combine like terms: 382 + -382 = 0 -382 + 64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-191 + 32t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-191 + 32t + -8t2)' equal to zero and attempt to solve: Simplifying -191 + 32t + -8t2 = 0 Solving -191 + 32t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 23.875 + -4t + t2 = 0 Move the constant term to the right: Add '-23.875' to each side of the equation. 23.875 + -4t + -23.875 + t2 = 0 + -23.875 Reorder the terms: 23.875 + -23.875 + -4t + t2 = 0 + -23.875 Combine like terms: 23.875 + -23.875 = 0.000 0.000 + -4t + t2 = 0 + -23.875 -4t + t2 = 0 + -23.875 Combine like terms: 0 + -23.875 = -23.875 -4t + t2 = -23.875 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -23.875 + 4 Reorder the terms: 4 + -4t + t2 = -23.875 + 4 Combine like terms: -23.875 + 4 = -19.875 4 + -4t + t2 = -19.875 Factor a perfect square on the left side: (t + -2)(t + -2) = -19.875 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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