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Simplifying 0 = 2t2 + -84t + 1025 Reorder the terms: 0 = 1025 + -84t + 2t2 Solving 0 = 1025 + -84t + 2t2 Solving for variable 't'. Combine like terms: 0 + -1025 = -1025 -1025 + 84t + -2t2 = 1025 + -84t + 2t2 + -1025 + 84t + -2t2 Reorder the terms: -1025 + 84t + -2t2 = 1025 + -1025 + -84t + 84t + 2t2 + -2t2 Combine like terms: 1025 + -1025 = 0 -1025 + 84t + -2t2 = 0 + -84t + 84t + 2t2 + -2t2 -1025 + 84t + -2t2 = -84t + 84t + 2t2 + -2t2 Combine like terms: -84t + 84t = 0 -1025 + 84t + -2t2 = 0 + 2t2 + -2t2 -1025 + 84t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -1025 + 84t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 512.5 + -42t + t2 = 0 Move the constant term to the right: Add '-512.5' to each side of the equation. 512.5 + -42t + -512.5 + t2 = 0 + -512.5 Reorder the terms: 512.5 + -512.5 + -42t + t2 = 0 + -512.5 Combine like terms: 512.5 + -512.5 = 0.0 0.0 + -42t + t2 = 0 + -512.5 -42t + t2 = 0 + -512.5 Combine like terms: 0 + -512.5 = -512.5 -42t + t2 = -512.5 The t term is -42t. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42t + 441 + t2 = -512.5 + 441 Reorder the terms: 441 + -42t + t2 = -512.5 + 441 Combine like terms: -512.5 + 441 = -71.5 441 + -42t + t2 = -71.5 Factor a perfect square on the left side: (t + -21)(t + -21) = -71.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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