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Simplifying v2 + v + -55 = 5v Reorder the terms: -55 + v + v2 = 5v Solving -55 + v + v2 = 5v Solving for variable 'v'. Reorder the terms: -55 + v + -5v + v2 = 5v + -5v Combine like terms: v + -5v = -4v -55 + -4v + v2 = 5v + -5v Combine like terms: 5v + -5v = 0 -55 + -4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -4v + 55 + v2 = 0 + 55 Reorder the terms: -55 + 55 + -4v + v2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -4v + v2 = 0 + 55 -4v + v2 = 0 + 55 Combine like terms: 0 + 55 = 55 -4v + v2 = 55 The v term is -4v. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4v + 4 + v2 = 55 + 4 Reorder the terms: 4 + -4v + v2 = 55 + 4 Combine like terms: 55 + 4 = 59 4 + -4v + v2 = 59 Factor a perfect square on the left side: (v + -2)(v + -2) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (v + -2) equal to 7.681145748 and -7.681145748.Subproblem 1
v + -2 = 7.681145748 Simplifying v + -2 = 7.681145748 Reorder the terms: -2 + v = 7.681145748 Solving -2 + v = 7.681145748 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = 7.681145748 + 2 Combine like terms: -2 + 2 = 0 0 + v = 7.681145748 + 2 v = 7.681145748 + 2 Combine like terms: 7.681145748 + 2 = 9.681145748 v = 9.681145748 Simplifying v = 9.681145748Subproblem 2
v + -2 = -7.681145748 Simplifying v + -2 = -7.681145748 Reorder the terms: -2 + v = -7.681145748 Solving -2 + v = -7.681145748 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = -7.681145748 + 2 Combine like terms: -2 + 2 = 0 0 + v = -7.681145748 + 2 v = -7.681145748 + 2 Combine like terms: -7.681145748 + 2 = -5.681145748 v = -5.681145748 Simplifying v = -5.681145748Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.681145748, -5.681145748}
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