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Simplifying v2 + -12v + 14 = 0 Reorder the terms: 14 + -12v + v2 = 0 Solving 14 + -12v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -12v + -14 + v2 = 0 + -14 Reorder the terms: 14 + -14 + -12v + v2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -12v + v2 = 0 + -14 -12v + v2 = 0 + -14 Combine like terms: 0 + -14 = -14 -12v + v2 = -14 The v term is -12v. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12v + 36 + v2 = -14 + 36 Reorder the terms: 36 + -12v + v2 = -14 + 36 Combine like terms: -14 + 36 = 22 36 + -12v + v2 = 22 Factor a perfect square on the left side: (v + -6)(v + -6) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (v + -6) equal to 4.69041576 and -4.69041576.Subproblem 1
v + -6 = 4.69041576 Simplifying v + -6 = 4.69041576 Reorder the terms: -6 + v = 4.69041576 Solving -6 + v = 4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 4.69041576 + 6 Combine like terms: -6 + 6 = 0 0 + v = 4.69041576 + 6 v = 4.69041576 + 6 Combine like terms: 4.69041576 + 6 = 10.69041576 v = 10.69041576 Simplifying v = 10.69041576Subproblem 2
v + -6 = -4.69041576 Simplifying v + -6 = -4.69041576 Reorder the terms: -6 + v = -4.69041576 Solving -6 + v = -4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = -4.69041576 + 6 Combine like terms: -6 + 6 = 0 0 + v = -4.69041576 + 6 v = -4.69041576 + 6 Combine like terms: -4.69041576 + 6 = 1.30958424 v = 1.30958424 Simplifying v = 1.30958424Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.69041576, 1.30958424}
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