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Simplifying 40 + v * 3(5 + v) = 2 Reorder the terms for easier multiplication: 40 + 3v(5 + v) = 2 40 + (5 * 3v + v * 3v) = 2 40 + (15v + 3v2) = 2 Solving 40 + 15v + 3v2 = 2 Solving for variable 'v'. Reorder the terms: 40 + -2 + 15v + 3v2 = 2 + -2 Combine like terms: 40 + -2 = 38 38 + 15v + 3v2 = 2 + -2 Combine like terms: 2 + -2 = 0 38 + 15v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 12.66666667 + 5v + v2 = 0 Move the constant term to the right: Add '-12.66666667' to each side of the equation. 12.66666667 + 5v + -12.66666667 + v2 = 0 + -12.66666667 Reorder the terms: 12.66666667 + -12.66666667 + 5v + v2 = 0 + -12.66666667 Combine like terms: 12.66666667 + -12.66666667 = 0.00000000 0.00000000 + 5v + v2 = 0 + -12.66666667 5v + v2 = 0 + -12.66666667 Combine like terms: 0 + -12.66666667 = -12.66666667 5v + v2 = -12.66666667 The v term is 5v. 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. 5v + 6.25 + v2 = -12.66666667 + 6.25 Reorder the terms: 6.25 + 5v + v2 = -12.66666667 + 6.25 Combine like terms: -12.66666667 + 6.25 = -6.41666667 6.25 + 5v + v2 = -6.41666667 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = -6.41666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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