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Simplifying v2 + -8v = 43 Reorder the terms: -8v + v2 = 43 Solving -8v + v2 = 43 Solving for variable 'v'. Reorder the terms: -43 + -8v + v2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -8v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -8v + 43 + v2 = 0 + 43 Reorder the terms: -43 + 43 + -8v + v2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -8v + v2 = 0 + 43 -8v + v2 = 0 + 43 Combine like terms: 0 + 43 = 43 -8v + v2 = 43 The v term is -8v. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8v + 16 + v2 = 43 + 16 Reorder the terms: 16 + -8v + v2 = 43 + 16 Combine like terms: 43 + 16 = 59 16 + -8v + v2 = 59 Factor a perfect square on the left side: (v + -4)(v + -4) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (v + -4) equal to 7.681145748 and -7.681145748.Subproblem 1
v + -4 = 7.681145748 Simplifying v + -4 = 7.681145748 Reorder the terms: -4 + v = 7.681145748 Solving -4 + v = 7.681145748 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = 7.681145748 + 4 Combine like terms: -4 + 4 = 0 0 + v = 7.681145748 + 4 v = 7.681145748 + 4 Combine like terms: 7.681145748 + 4 = 11.681145748 v = 11.681145748 Simplifying v = 11.681145748Subproblem 2
v + -4 = -7.681145748 Simplifying v + -4 = -7.681145748 Reorder the terms: -4 + v = -7.681145748 Solving -4 + v = -7.681145748 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = -7.681145748 + 4 Combine like terms: -4 + 4 = 0 0 + v = -7.681145748 + 4 v = -7.681145748 + 4 Combine like terms: -7.681145748 + 4 = -3.681145748 v = -3.681145748 Simplifying v = -3.681145748Solution
The solution to the problem is based on the solutions from the subproblems. v = {11.681145748, -3.681145748}
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