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Simplifying -4v(v + -2) = -4(v + -8) + -8v Reorder the terms: -4v(-2 + v) = -4(v + -8) + -8v (-2 * -4v + v * -4v) = -4(v + -8) + -8v (8v + -4v2) = -4(v + -8) + -8v Reorder the terms: 8v + -4v2 = -4(-8 + v) + -8v 8v + -4v2 = (-8 * -4 + v * -4) + -8v 8v + -4v2 = (32 + -4v) + -8v Combine like terms: -4v + -8v = -12v 8v + -4v2 = 32 + -12v Solving 8v + -4v2 = 32 + -12v Solving for variable 'v'. Reorder the terms: -32 + 8v + 12v + -4v2 = 32 + -12v + -32 + 12v Combine like terms: 8v + 12v = 20v -32 + 20v + -4v2 = 32 + -12v + -32 + 12v Reorder the terms: -32 + 20v + -4v2 = 32 + -32 + -12v + 12v Combine like terms: 32 + -32 = 0 -32 + 20v + -4v2 = 0 + -12v + 12v -32 + 20v + -4v2 = -12v + 12v Combine like terms: -12v + 12v = 0 -32 + 20v + -4v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 5v + -1v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 5v + -1v2)' equal to zero and attempt to solve: Simplifying -8 + 5v + -1v2 = 0 Solving -8 + 5v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -5v + v2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5v + -8 + v2 = 0 + -8 Reorder the terms: 8 + -8 + -5v + v2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5v + v2 = 0 + -8 -5v + v2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5v + v2 = -8 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 = -8 + 6.25 Reorder the terms: 6.25 + -5v + v2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5v + v2 = -1.75 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = -1.75 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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