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Simplifying v2 + -14v + 27 = 0 Reorder the terms: 27 + -14v + v2 = 0 Solving 27 + -14v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -14v + -27 + v2 = 0 + -27 Reorder the terms: 27 + -27 + -14v + v2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -14v + v2 = 0 + -27 -14v + v2 = 0 + -27 Combine like terms: 0 + -27 = -27 -14v + v2 = -27 The v term is -14v. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14v + 49 + v2 = -27 + 49 Reorder the terms: 49 + -14v + v2 = -27 + 49 Combine like terms: -27 + 49 = 22 49 + -14v + v2 = 22 Factor a perfect square on the left side: (v + -7)(v + -7) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (v + -7) equal to 4.69041576 and -4.69041576.Subproblem 1
v + -7 = 4.69041576 Simplifying v + -7 = 4.69041576 Reorder the terms: -7 + v = 4.69041576 Solving -7 + v = 4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = 4.69041576 + 7 Combine like terms: -7 + 7 = 0 0 + v = 4.69041576 + 7 v = 4.69041576 + 7 Combine like terms: 4.69041576 + 7 = 11.69041576 v = 11.69041576 Simplifying v = 11.69041576Subproblem 2
v + -7 = -4.69041576 Simplifying v + -7 = -4.69041576 Reorder the terms: -7 + v = -4.69041576 Solving -7 + v = -4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = -4.69041576 + 7 Combine like terms: -7 + 7 = 0 0 + v = -4.69041576 + 7 v = -4.69041576 + 7 Combine like terms: -4.69041576 + 7 = 2.30958424 v = 2.30958424 Simplifying v = 2.30958424Solution
The solution to the problem is based on the solutions from the subproblems. v = {11.69041576, 2.30958424}
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