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Simplifying t(t + 5) = 2t2 + 7 Reorder the terms: t(5 + t) = 2t2 + 7 (5 * t + t * t) = 2t2 + 7 (5t + t2) = 2t2 + 7 Reorder the terms: 5t + t2 = 7 + 2t2 Solving 5t + t2 = 7 + 2t2 Solving for variable 't'. Reorder the terms: -7 + 5t + t2 + -2t2 = 7 + 2t2 + -7 + -2t2 Combine like terms: t2 + -2t2 = -1t2 -7 + 5t + -1t2 = 7 + 2t2 + -7 + -2t2 Reorder the terms: -7 + 5t + -1t2 = 7 + -7 + 2t2 + -2t2 Combine like terms: 7 + -7 = 0 -7 + 5t + -1t2 = 0 + 2t2 + -2t2 -7 + 5t + -1t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -7 + 5t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -5t + t2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -5t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -5t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5t + t2 = 0 + -7 -5t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -5t + t2 = -7 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -7 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -7 + 6.25 Combine like terms: -7 + 6.25 = -0.75 6.25 + -5t + t2 = -0.75 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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