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Simplifying -7v2 = 1 + 5v Solving -7v2 = 1 + 5v Solving for variable 'v'. Reorder the terms: -1 + -5v + -7v2 = 1 + 5v + -1 + -5v Reorder the terms: -1 + -5v + -7v2 = 1 + -1 + 5v + -5v Combine like terms: 1 + -1 = 0 -1 + -5v + -7v2 = 0 + 5v + -5v -1 + -5v + -7v2 = 5v + -5v Combine like terms: 5v + -5v = 0 -1 + -5v + -7v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 5v + 7v2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 5v + 7v2)' equal to zero and attempt to solve: Simplifying 1 + 5v + 7v2 = 0 Solving 1 + 5v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.7142857143v + v2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.7142857143v + -0.1428571429 + v2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.7142857143v + v2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.7142857143v + v2 = 0 + -0.1428571429 0.7142857143v + v2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.7142857143v + v2 = -0.1428571429 The v term is 0.7142857143v. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143v + 0.1275510204 + v2 = -0.1428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143v + v2 = -0.1428571429 + 0.1275510204 Combine like terms: -0.1428571429 + 0.1275510204 = -0.0153061225 0.1275510204 + 0.7142857143v + v2 = -0.0153061225 Factor a perfect square on the left side: (v + 0.3571428572)(v + 0.3571428572) = -0.0153061225 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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