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Simplifying v2 + -8v = 21 Reorder the terms: -8v + v2 = 21 Solving -8v + v2 = 21 Solving for variable 'v'. Reorder the terms: -21 + -8v + v2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -8v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -8v + 21 + v2 = 0 + 21 Reorder the terms: -21 + 21 + -8v + v2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -8v + v2 = 0 + 21 -8v + v2 = 0 + 21 Combine like terms: 0 + 21 = 21 -8v + v2 = 21 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 = 21 + 16 Reorder the terms: 16 + -8v + v2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + -8v + v2 = 37 Factor a perfect square on the left side: (v + -4)(v + -4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (v + -4) equal to 6.08276253 and -6.08276253.Subproblem 1
v + -4 = 6.08276253 Simplifying v + -4 = 6.08276253 Reorder the terms: -4 + v = 6.08276253 Solving -4 + v = 6.08276253 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 = 6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + v = 6.08276253 + 4 v = 6.08276253 + 4 Combine like terms: 6.08276253 + 4 = 10.08276253 v = 10.08276253 Simplifying v = 10.08276253Subproblem 2
v + -4 = -6.08276253 Simplifying v + -4 = -6.08276253 Reorder the terms: -4 + v = -6.08276253 Solving -4 + v = -6.08276253 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 = -6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + v = -6.08276253 + 4 v = -6.08276253 + 4 Combine like terms: -6.08276253 + 4 = -2.08276253 v = -2.08276253 Simplifying v = -2.08276253Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.08276253, -2.08276253}
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