v+7v-2v^2=30

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Solution for v+7v-2v^2=30 equation:


Simplifying
v + 7v + -2v2 = 30

Combine like terms: v + 7v = 8v
8v + -2v2 = 30

Solving
8v + -2v2 = 30

Solving for variable 'v'.

Reorder the terms:
-30 + 8v + -2v2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 8v + -2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 4v + -1v2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-15 + 4v + -1v2)' equal to zero and attempt to solve: Simplifying -15 + 4v + -1v2 = 0 Solving -15 + 4v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15 + -4v + v2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -4v + -15 + v2 = 0 + -15 Reorder the terms: 15 + -15 + -4v + v2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4v + v2 = 0 + -15 -4v + v2 = 0 + -15 Combine like terms: 0 + -15 = -15 -4v + v2 = -15 The v term is -4v. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4v + 4 + v2 = -15 + 4 Reorder the terms: 4 + -4v + v2 = -15 + 4 Combine like terms: -15 + 4 = -11 4 + -4v + v2 = -11 Factor a perfect square on the left side: (v + -2)(v + -2) = -11 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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