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Simplifying 4v2 + -120v = 44 Reorder the terms: -120v + 4v2 = 44 Solving -120v + 4v2 = 44 Solving for variable 'v'. Reorder the terms: -44 + -120v + 4v2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -120v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + -30v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + -30v + v2)' equal to zero and attempt to solve: Simplifying -11 + -30v + v2 = 0 Solving -11 + -30v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -30v + 11 + v2 = 0 + 11 Reorder the terms: -11 + 11 + -30v + v2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -30v + v2 = 0 + 11 -30v + v2 = 0 + 11 Combine like terms: 0 + 11 = 11 -30v + v2 = 11 The v term is -30v. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30v + 225 + v2 = 11 + 225 Reorder the terms: 225 + -30v + v2 = 11 + 225 Combine like terms: 11 + 225 = 236 225 + -30v + v2 = 236 Factor a perfect square on the left side: (v + -15)(v + -15) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (v + -15) equal to 15.362291496 and -15.362291496.Subproblem 1
v + -15 = 15.362291496 Simplifying v + -15 = 15.362291496 Reorder the terms: -15 + v = 15.362291496 Solving -15 + v = 15.362291496 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + v = 15.362291496 + 15 Combine like terms: -15 + 15 = 0 0 + v = 15.362291496 + 15 v = 15.362291496 + 15 Combine like terms: 15.362291496 + 15 = 30.362291496 v = 30.362291496 Simplifying v = 30.362291496Subproblem 2
v + -15 = -15.362291496 Simplifying v + -15 = -15.362291496 Reorder the terms: -15 + v = -15.362291496 Solving -15 + v = -15.362291496 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + v = -15.362291496 + 15 Combine like terms: -15 + 15 = 0 0 + v = -15.362291496 + 15 v = -15.362291496 + 15 Combine like terms: -15.362291496 + 15 = -0.362291496 v = -0.362291496 Simplifying v = -0.362291496Solution
The solution to the problem is based on the solutions from the subproblems. v = {30.362291496, -0.362291496}Solution
v = {30.362291496, -0.362291496}
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