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Simplifying v = 20.8v2 + -458.3v + 3500 Reorder the terms: v = 3500 + -458.3v + 20.8v2 Solving v = 3500 + -458.3v + 20.8v2 Solving for variable 'v'. Reorder the terms: -3500 + v + 458.3v + -20.8v2 = 3500 + -458.3v + 20.8v2 + -3500 + 458.3v + -20.8v2 Combine like terms: v + 458.3v = 459.3v -3500 + 459.3v + -20.8v2 = 3500 + -458.3v + 20.8v2 + -3500 + 458.3v + -20.8v2 Reorder the terms: -3500 + 459.3v + -20.8v2 = 3500 + -3500 + -458.3v + 458.3v + 20.8v2 + -20.8v2 Combine like terms: 3500 + -3500 = 0 -3500 + 459.3v + -20.8v2 = 0 + -458.3v + 458.3v + 20.8v2 + -20.8v2 -3500 + 459.3v + -20.8v2 = -458.3v + 458.3v + 20.8v2 + -20.8v2 Combine like terms: -458.3v + 458.3v = 0.0 -3500 + 459.3v + -20.8v2 = 0.0 + 20.8v2 + -20.8v2 -3500 + 459.3v + -20.8v2 = 20.8v2 + -20.8v2 Combine like terms: 20.8v2 + -20.8v2 = 0.0 -3500 + 459.3v + -20.8v2 = 0.0 Begin completing the square. Divide all terms by -20.8 the coefficient of the squared term: Divide each side by '-20.8'. 168.2692308 + -22.08173077v + v2 = 0 Move the constant term to the right: Add '-168.2692308' to each side of the equation. 168.2692308 + -22.08173077v + -168.2692308 + v2 = 0 + -168.2692308 Reorder the terms: 168.2692308 + -168.2692308 + -22.08173077v + v2 = 0 + -168.2692308 Combine like terms: 168.2692308 + -168.2692308 = 0.0000000 0.0000000 + -22.08173077v + v2 = 0 + -168.2692308 -22.08173077v + v2 = 0 + -168.2692308 Combine like terms: 0 + -168.2692308 = -168.2692308 -22.08173077v + v2 = -168.2692308 The v term is -22.08173077v. Take half its coefficient (-11.04086539). Square it (121.9007086) and add it to both sides. Add '121.9007086' to each side of the equation. -22.08173077v + 121.9007086 + v2 = -168.2692308 + 121.9007086 Reorder the terms: 121.9007086 + -22.08173077v + v2 = -168.2692308 + 121.9007086 Combine like terms: -168.2692308 + 121.9007086 = -46.3685222 121.9007086 + -22.08173077v + v2 = -46.3685222 Factor a perfect square on the left side: (v + -11.04086539)(v + -11.04086539) = -46.3685222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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