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Simplifying -3v2 + -6v = -141 Reorder the terms: -6v + -3v2 = -141 Solving -6v + -3v2 = -141 Solving for variable 'v'. Reorder the terms: 141 + -6v + -3v2 = -141 + 141 Combine like terms: -141 + 141 = 0 141 + -6v + -3v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(47 + -2v + -1v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(47 + -2v + -1v2)' equal to zero and attempt to solve: Simplifying 47 + -2v + -1v2 = 0 Solving 47 + -2v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 2v + v2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 2v + 47 + v2 = 0 + 47 Reorder the terms: -47 + 47 + 2v + v2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2v + v2 = 0 + 47 2v + v2 = 0 + 47 Combine like terms: 0 + 47 = 47 2v + v2 = 47 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 + v2 = 47 + 1 Reorder the terms: 1 + 2v + v2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2v + v2 = 48 Factor a perfect square on the left side: (v + 1)(v + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (v + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
v + 1 = 6.92820323 Simplifying v + 1 = 6.92820323 Reorder the terms: 1 + v = 6.92820323 Solving 1 + v = 6.92820323 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + v = 6.92820323 + -1 v = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 v = 5.92820323 Simplifying v = 5.92820323Subproblem 2
v + 1 = -6.92820323 Simplifying v + 1 = -6.92820323 Reorder the terms: 1 + v = -6.92820323 Solving 1 + v = -6.92820323 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + v = -6.92820323 + -1 v = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 v = -7.92820323 Simplifying v = -7.92820323Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.92820323, -7.92820323}Solution
v = {5.92820323, -7.92820323}
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