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Simplifying v2 + 8v + -59 = 0 Reorder the terms: -59 + 8v + v2 = 0 Solving -59 + 8v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 8v + 59 + v2 = 0 + 59 Reorder the terms: -59 + 59 + 8v + v2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 8v + v2 = 0 + 59 8v + v2 = 0 + 59 Combine like terms: 0 + 59 = 59 8v + v2 = 59 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 = 59 + 16 Reorder the terms: 16 + 8v + v2 = 59 + 16 Combine like terms: 59 + 16 = 75 16 + 8v + v2 = 75 Factor a perfect square on the left side: (v + 4)(v + 4) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (v + 4) equal to 8.660254038 and -8.660254038.Subproblem 1
v + 4 = 8.660254038 Simplifying v + 4 = 8.660254038 Reorder the terms: 4 + v = 8.660254038 Solving 4 + v = 8.660254038 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 = 8.660254038 + -4 Combine like terms: 4 + -4 = 0 0 + v = 8.660254038 + -4 v = 8.660254038 + -4 Combine like terms: 8.660254038 + -4 = 4.660254038 v = 4.660254038 Simplifying v = 4.660254038Subproblem 2
v + 4 = -8.660254038 Simplifying v + 4 = -8.660254038 Reorder the terms: 4 + v = -8.660254038 Solving 4 + v = -8.660254038 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 = -8.660254038 + -4 Combine like terms: 4 + -4 = 0 0 + v = -8.660254038 + -4 v = -8.660254038 + -4 Combine like terms: -8.660254038 + -4 = -12.660254038 v = -12.660254038 Simplifying v = -12.660254038Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.660254038, -12.660254038}
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