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Simplifying 2v3 + -84v2 + -80v = 0 Reorder the terms: -80v + -84v2 + 2v3 = 0 Solving -80v + -84v2 + 2v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2v'. 2v(-40 + -42v + v2) = 0 Ignore the factor 2.Subproblem 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 '(-40 + -42v + v2)' equal to zero and attempt to solve: Simplifying -40 + -42v + v2 = 0 Solving -40 + -42v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -42v + 40 + v2 = 0 + 40 Reorder the terms: -40 + 40 + -42v + v2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -42v + v2 = 0 + 40 -42v + v2 = 0 + 40 Combine like terms: 0 + 40 = 40 -42v + v2 = 40 The v term is -42v. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42v + 441 + v2 = 40 + 441 Reorder the terms: 441 + -42v + v2 = 40 + 441 Combine like terms: 40 + 441 = 481 441 + -42v + v2 = 481 Factor a perfect square on the left side: (v + -21)(v + -21) = 481 Calculate the square root of the right side: 21.931712199 Break this problem into two subproblems by setting (v + -21) equal to 21.931712199 and -21.931712199.Subproblem 1
v + -21 = 21.931712199 Simplifying v + -21 = 21.931712199 Reorder the terms: -21 + v = 21.931712199 Solving -21 + v = 21.931712199 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + v = 21.931712199 + 21 Combine like terms: -21 + 21 = 0 0 + v = 21.931712199 + 21 v = 21.931712199 + 21 Combine like terms: 21.931712199 + 21 = 42.931712199 v = 42.931712199 Simplifying v = 42.931712199Subproblem 2
v + -21 = -21.931712199 Simplifying v + -21 = -21.931712199 Reorder the terms: -21 + v = -21.931712199 Solving -21 + v = -21.931712199 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + v = -21.931712199 + 21 Combine like terms: -21 + 21 = 0 0 + v = -21.931712199 + 21 v = -21.931712199 + 21 Combine like terms: -21.931712199 + 21 = -0.931712199 v = -0.931712199 Simplifying v = -0.931712199Solution
The solution to the problem is based on the solutions from the subproblems. v = {42.931712199, -0.931712199}Solution
v = {0, 42.931712199, -0.931712199}
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