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Simplifying v2 + -27v = 16 Reorder the terms: -27v + v2 = 16 Solving -27v + v2 = 16 Solving for variable 'v'. Reorder the terms: -16 + -27v + v2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -27v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -27v + 16 + v2 = 0 + 16 Reorder the terms: -16 + 16 + -27v + v2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -27v + v2 = 0 + 16 -27v + v2 = 0 + 16 Combine like terms: 0 + 16 = 16 -27v + v2 = 16 The v term is -27v. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27v + 182.25 + v2 = 16 + 182.25 Reorder the terms: 182.25 + -27v + v2 = 16 + 182.25 Combine like terms: 16 + 182.25 = 198.25 182.25 + -27v + v2 = 198.25 Factor a perfect square on the left side: (v + -13.5)(v + -13.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (v + -13.5) equal to 14.08012784 and -14.08012784.Subproblem 1
v + -13.5 = 14.08012784 Simplifying v + -13.5 = 14.08012784 Reorder the terms: -13.5 + v = 14.08012784 Solving -13.5 + v = 14.08012784 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + v = 14.08012784 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + v = 14.08012784 + 13.5 v = 14.08012784 + 13.5 Combine like terms: 14.08012784 + 13.5 = 27.58012784 v = 27.58012784 Simplifying v = 27.58012784Subproblem 2
v + -13.5 = -14.08012784 Simplifying v + -13.5 = -14.08012784 Reorder the terms: -13.5 + v = -14.08012784 Solving -13.5 + v = -14.08012784 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + v = -14.08012784 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + v = -14.08012784 + 13.5 v = -14.08012784 + 13.5 Combine like terms: -14.08012784 + 13.5 = -0.58012784 v = -0.58012784 Simplifying v = -0.58012784Solution
The solution to the problem is based on the solutions from the subproblems. v = {27.58012784, -0.58012784}
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