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Simplifying t = 16t2 + 500 Reorder the terms: t = 500 + 16t2 Solving t = 500 + 16t2 Solving for variable 't'. Reorder the terms: -500 + t + -16t2 = 500 + 16t2 + -500 + -16t2 Reorder the terms: -500 + t + -16t2 = 500 + -500 + 16t2 + -16t2 Combine like terms: 500 + -500 = 0 -500 + t + -16t2 = 0 + 16t2 + -16t2 -500 + t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -500 + t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 31.25 + -0.0625t + t2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + -0.0625t + -31.25 + t2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + -0.0625t + t2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + -0.0625t + t2 = 0 + -31.25 -0.0625t + t2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 -0.0625t + t2 = -31.25 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. -0.0625t + 0.25 + t2 = -31.25 + 0.25 Reorder the terms: 0.25 + -0.0625t + t2 = -31.25 + 0.25 Combine like terms: -31.25 + 0.25 = -31 0.25 + -0.0625t + t2 = -31 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -31 Can't calculate square root of the right side. The solution to this equation could not be determined.
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