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Simplifying 3(v2 + -2v + -19) = 0 Reorder the terms: 3(-19 + -2v + v2) = 0 (-19 * 3 + -2v * 3 + v2 * 3) = 0 (-57 + -6v + 3v2) = 0 Solving -57 + -6v + 3v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(-19 + -2v + v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-19 + -2v + v2)' equal to zero and attempt to solve: Simplifying -19 + -2v + v2 = 0 Solving -19 + -2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -2v + 19 + v2 = 0 + 19 Reorder the terms: -19 + 19 + -2v + v2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2v + v2 = 0 + 19 -2v + v2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2v + v2 = 19 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 = 19 + 1 Reorder the terms: 1 + -2v + v2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + -2v + v2 = 20 Factor a perfect square on the left side: (v + -1)(v + -1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (v + -1) equal to 4.472135955 and -4.472135955.Subproblem 1
v + -1 = 4.472135955 Simplifying v + -1 = 4.472135955 Reorder the terms: -1 + v = 4.472135955 Solving -1 + v = 4.472135955 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 = 4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + v = 4.472135955 + 1 v = 4.472135955 + 1 Combine like terms: 4.472135955 + 1 = 5.472135955 v = 5.472135955 Simplifying v = 5.472135955Subproblem 2
v + -1 = -4.472135955 Simplifying v + -1 = -4.472135955 Reorder the terms: -1 + v = -4.472135955 Solving -1 + v = -4.472135955 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 = -4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + v = -4.472135955 + 1 v = -4.472135955 + 1 Combine like terms: -4.472135955 + 1 = -3.472135955 v = -3.472135955 Simplifying v = -3.472135955Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.472135955, -3.472135955}Solution
v = {5.472135955, -3.472135955}
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