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Simplifying v2 + -14v + -76 = 6 Reorder the terms: -76 + -14v + v2 = 6 Solving -76 + -14v + v2 = 6 Solving for variable 'v'. Reorder the terms: -76 + -6 + -14v + v2 = 6 + -6 Combine like terms: -76 + -6 = -82 -82 + -14v + v2 = 6 + -6 Combine like terms: 6 + -6 = 0 -82 + -14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -14v + 82 + v2 = 0 + 82 Reorder the terms: -82 + 82 + -14v + v2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -14v + v2 = 0 + 82 -14v + v2 = 0 + 82 Combine like terms: 0 + 82 = 82 -14v + v2 = 82 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 = 82 + 49 Reorder the terms: 49 + -14v + v2 = 82 + 49 Combine like terms: 82 + 49 = 131 49 + -14v + v2 = 131 Factor a perfect square on the left side: (v + -7)(v + -7) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (v + -7) equal to 11.445523142 and -11.445523142.Subproblem 1
v + -7 = 11.445523142 Simplifying v + -7 = 11.445523142 Reorder the terms: -7 + v = 11.445523142 Solving -7 + v = 11.445523142 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 = 11.445523142 + 7 Combine like terms: -7 + 7 = 0 0 + v = 11.445523142 + 7 v = 11.445523142 + 7 Combine like terms: 11.445523142 + 7 = 18.445523142 v = 18.445523142 Simplifying v = 18.445523142Subproblem 2
v + -7 = -11.445523142 Simplifying v + -7 = -11.445523142 Reorder the terms: -7 + v = -11.445523142 Solving -7 + v = -11.445523142 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 = -11.445523142 + 7 Combine like terms: -7 + 7 = 0 0 + v = -11.445523142 + 7 v = -11.445523142 + 7 Combine like terms: -11.445523142 + 7 = -4.445523142 v = -4.445523142 Simplifying v = -4.445523142Solution
The solution to the problem is based on the solutions from the subproblems. v = {18.445523142, -4.445523142}
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