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Simplifying -4v(v + 6) = -16 Reorder the terms: -4v(6 + v) = -16 (6 * -4v + v * -4v) = -16 (-24v + -4v2) = -16 Solving -24v + -4v2 = -16 Solving for variable 'v'. Reorder the terms: 16 + -24v + -4v2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -24v + -4v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -6v + -1v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -6v + -1v2)' equal to zero and attempt to solve: Simplifying 4 + -6v + -1v2 = 0 Solving 4 + -6v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 6v + v2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 6v + 4 + v2 = 0 + 4 Reorder the terms: -4 + 4 + 6v + v2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6v + v2 = 0 + 4 6v + v2 = 0 + 4 Combine like terms: 0 + 4 = 4 6v + v2 = 4 The v term is 6v. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6v + 9 + v2 = 4 + 9 Reorder the terms: 9 + 6v + v2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6v + v2 = 13 Factor a perfect square on the left side: (v + 3)(v + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (v + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
v + 3 = 3.605551275 Simplifying v + 3 = 3.605551275 Reorder the terms: 3 + v = 3.605551275 Solving 3 + v = 3.605551275 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + v = 3.605551275 + -3 v = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 v = 0.605551275 Simplifying v = 0.605551275Subproblem 2
v + 3 = -3.605551275 Simplifying v + 3 = -3.605551275 Reorder the terms: 3 + v = -3.605551275 Solving 3 + v = -3.605551275 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + v = -3.605551275 + -3 v = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 v = -6.605551275 Simplifying v = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.605551275, -6.605551275}Solution
v = {0.605551275, -6.605551275}
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