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Simplifying v2 + -16v + -20 = 0 Reorder the terms: -20 + -16v + v2 = 0 Solving -20 + -16v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -16v + 20 + v2 = 0 + 20 Reorder the terms: -20 + 20 + -16v + v2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -16v + v2 = 0 + 20 -16v + v2 = 0 + 20 Combine like terms: 0 + 20 = 20 -16v + v2 = 20 The v term is -16v. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16v + 64 + v2 = 20 + 64 Reorder the terms: 64 + -16v + v2 = 20 + 64 Combine like terms: 20 + 64 = 84 64 + -16v + v2 = 84 Factor a perfect square on the left side: (v + -8)(v + -8) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (v + -8) equal to 9.16515139 and -9.16515139.Subproblem 1
v + -8 = 9.16515139 Simplifying v + -8 = 9.16515139 Reorder the terms: -8 + v = 9.16515139 Solving -8 + v = 9.16515139 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + v = 9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + v = 9.16515139 + 8 v = 9.16515139 + 8 Combine like terms: 9.16515139 + 8 = 17.16515139 v = 17.16515139 Simplifying v = 17.16515139Subproblem 2
v + -8 = -9.16515139 Simplifying v + -8 = -9.16515139 Reorder the terms: -8 + v = -9.16515139 Solving -8 + v = -9.16515139 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + v = -9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + v = -9.16515139 + 8 v = -9.16515139 + 8 Combine like terms: -9.16515139 + 8 = -1.16515139 v = -1.16515139 Simplifying v = -1.16515139Solution
The solution to the problem is based on the solutions from the subproblems. v = {17.16515139, -1.16515139}
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