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Simplifying 2v^{2}+ -4v + 52 = 0 Reorder the terms: 52 + -4v + 2v^{2}= 0 Solving 52 + -4v + 2v^{2}= 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -2v + v^{2}) = 0 Ignore the factor 2.## Subproblem 1

Set the factor '(26 + -2v + v^{2})' equal to zero and attempt to solve: Simplifying 26 + -2v + v^{2}= 0 Solving 26 + -2v + v^{2}= 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -2v + -26 + v^{2}= 0 + -26 Reorder the terms: 26 + -26 + -2v + v^{2}= 0 + -26 Combine like terms: 26 + -26 = 0 0 + -2v + v^{2}= 0 + -26 -2v + v^{2}= 0 + -26 Combine like terms: 0 + -26 = -26 -2v + v^{2}= -26 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v^{2}= -26 + 1 Reorder the terms: 1 + -2v + v^{2}= -26 + 1 Combine like terms: -26 + 1 = -25 1 + -2v + v^{2}= -25 Factor a perfect square on the left side: (v + -1)(v + -1) = -25 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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