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Simplifying v2 + 25 = 2v2 + -1v + 53 Reorder the terms: 25 + v2 = 2v2 + -1v + 53 Reorder the terms: 25 + v2 = 53 + -1v + 2v2 Solving 25 + v2 = 53 + -1v + 2v2 Solving for variable 'v'. Reorder the terms: 25 + -53 + v + v2 + -2v2 = 53 + -1v + 2v2 + -53 + v + -2v2 Combine like terms: 25 + -53 = -28 -28 + v + v2 + -2v2 = 53 + -1v + 2v2 + -53 + v + -2v2 Combine like terms: v2 + -2v2 = -1v2 -28 + v + -1v2 = 53 + -1v + 2v2 + -53 + v + -2v2 Reorder the terms: -28 + v + -1v2 = 53 + -53 + -1v + v + 2v2 + -2v2 Combine like terms: 53 + -53 = 0 -28 + v + -1v2 = 0 + -1v + v + 2v2 + -2v2 -28 + v + -1v2 = -1v + v + 2v2 + -2v2 Combine like terms: -1v + v = 0 -28 + v + -1v2 = 0 + 2v2 + -2v2 -28 + v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -28 + v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 28 + -1v + v2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -1v + -28 + v2 = 0 + -28 Reorder the terms: 28 + -28 + -1v + v2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -1v + v2 = 0 + -28 -1v + v2 = 0 + -28 Combine like terms: 0 + -28 = -28 -1v + v2 = -28 The v term is v. 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. -1v + 0.25 + v2 = -28 + 0.25 Reorder the terms: 0.25 + -1v + v2 = -28 + 0.25 Combine like terms: -28 + 0.25 = -27.75 0.25 + -1v + v2 = -27.75 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = -27.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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