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Simplifying v2 + 20v = -25 Reorder the terms: 20v + v2 = -25 Solving 20v + v2 = -25 Solving for variable 'v'. Reorder the terms: 25 + 20v + v2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 20v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 20v + -25 + v2 = 0 + -25 Reorder the terms: 25 + -25 + 20v + v2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 20v + v2 = 0 + -25 20v + v2 = 0 + -25 Combine like terms: 0 + -25 = -25 20v + v2 = -25 The v term is 20v. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20v + 100 + v2 = -25 + 100 Reorder the terms: 100 + 20v + v2 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + 20v + v2 = 75 Factor a perfect square on the left side: (v + 10)(v + 10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (v + 10) equal to 8.660254038 and -8.660254038.Subproblem 1
v + 10 = 8.660254038 Simplifying v + 10 = 8.660254038 Reorder the terms: 10 + v = 8.660254038 Solving 10 + v = 8.660254038 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + v = 8.660254038 + -10 Combine like terms: 10 + -10 = 0 0 + v = 8.660254038 + -10 v = 8.660254038 + -10 Combine like terms: 8.660254038 + -10 = -1.339745962 v = -1.339745962 Simplifying v = -1.339745962Subproblem 2
v + 10 = -8.660254038 Simplifying v + 10 = -8.660254038 Reorder the terms: 10 + v = -8.660254038 Solving 10 + v = -8.660254038 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + v = -8.660254038 + -10 Combine like terms: 10 + -10 = 0 0 + v = -8.660254038 + -10 v = -8.660254038 + -10 Combine like terms: -8.660254038 + -10 = -18.660254038 v = -18.660254038 Simplifying v = -18.660254038Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.339745962, -18.660254038}
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