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Simplifying 100 = 16t2 + 64t + 185 Reorder the terms: 100 = 185 + 64t + 16t2 Solving 100 = 185 + 64t + 16t2 Solving for variable 't'. Combine like terms: 100 + -185 = -85 -85 + -64t + -16t2 = 185 + 64t + 16t2 + -185 + -64t + -16t2 Reorder the terms: -85 + -64t + -16t2 = 185 + -185 + 64t + -64t + 16t2 + -16t2 Combine like terms: 185 + -185 = 0 -85 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2 -85 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -85 + -64t + -16t2 = 0 + 16t2 + -16t2 -85 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -85 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(85 + 64t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(85 + 64t + 16t2)' equal to zero and attempt to solve: Simplifying 85 + 64t + 16t2 = 0 Solving 85 + 64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.3125 + 4t + t2 = 0 Move the constant term to the right: Add '-5.3125' to each side of the equation. 5.3125 + 4t + -5.3125 + t2 = 0 + -5.3125 Reorder the terms: 5.3125 + -5.3125 + 4t + t2 = 0 + -5.3125 Combine like terms: 5.3125 + -5.3125 = 0.0000 0.0000 + 4t + t2 = 0 + -5.3125 4t + t2 = 0 + -5.3125 Combine like terms: 0 + -5.3125 = -5.3125 4t + t2 = -5.3125 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 = -5.3125 + 4 Reorder the terms: 4 + 4t + t2 = -5.3125 + 4 Combine like terms: -5.3125 + 4 = -1.3125 4 + 4t + t2 = -1.3125 Factor a perfect square on the left side: (t + 2)(t + 2) = -1.3125 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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