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Simplifying v3 + 14v2 + -48v = 0 Reorder the terms: -48v + 14v2 + v3 = 0 Solving -48v + 14v2 + v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(-48 + 14v + v2) = 0Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-48 + 14v + v2)' equal to zero and attempt to solve: Simplifying -48 + 14v + v2 = 0 Solving -48 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 14v + 48 + v2 = 0 + 48 Reorder the terms: -48 + 48 + 14v + v2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 14v + v2 = 0 + 48 14v + v2 = 0 + 48 Combine like terms: 0 + 48 = 48 14v + v2 = 48 The v term is 14v. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14v + 49 + v2 = 48 + 49 Reorder the terms: 49 + 14v + v2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + 14v + v2 = 97 Factor a perfect square on the left side: (v + 7)(v + 7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (v + 7) equal to 9.848857802 and -9.848857802.Subproblem 1
v + 7 = 9.848857802 Simplifying v + 7 = 9.848857802 Reorder the terms: 7 + v = 9.848857802 Solving 7 + v = 9.848857802 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + v = 9.848857802 + -7 v = 9.848857802 + -7 Combine like terms: 9.848857802 + -7 = 2.848857802 v = 2.848857802 Simplifying v = 2.848857802Subproblem 2
v + 7 = -9.848857802 Simplifying v + 7 = -9.848857802 Reorder the terms: 7 + v = -9.848857802 Solving 7 + v = -9.848857802 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = -9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + v = -9.848857802 + -7 v = -9.848857802 + -7 Combine like terms: -9.848857802 + -7 = -16.848857802 v = -16.848857802 Simplifying v = -16.848857802Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.848857802, -16.848857802}Solution
v = {0, 2.848857802, -16.848857802}
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