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Simplifying v2 + -8v + -78 = 4 Reorder the terms: -78 + -8v + v2 = 4 Solving -78 + -8v + v2 = 4 Solving for variable 'v'. Reorder the terms: -78 + -4 + -8v + v2 = 4 + -4 Combine like terms: -78 + -4 = -82 -82 + -8v + v2 = 4 + -4 Combine like terms: 4 + -4 = 0 -82 + -8v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -8v + 82 + v2 = 0 + 82 Reorder the terms: -82 + 82 + -8v + v2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -8v + v2 = 0 + 82 -8v + v2 = 0 + 82 Combine like terms: 0 + 82 = 82 -8v + v2 = 82 The v term is -8v. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8v + 16 + v2 = 82 + 16 Reorder the terms: 16 + -8v + v2 = 82 + 16 Combine like terms: 82 + 16 = 98 16 + -8v + v2 = 98 Factor a perfect square on the left side: (v + -4)(v + -4) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (v + -4) equal to 9.899494937 and -9.899494937.Subproblem 1
v + -4 = 9.899494937 Simplifying v + -4 = 9.899494937 Reorder the terms: -4 + v = 9.899494937 Solving -4 + v = 9.899494937 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = 9.899494937 + 4 Combine like terms: -4 + 4 = 0 0 + v = 9.899494937 + 4 v = 9.899494937 + 4 Combine like terms: 9.899494937 + 4 = 13.899494937 v = 13.899494937 Simplifying v = 13.899494937Subproblem 2
v + -4 = -9.899494937 Simplifying v + -4 = -9.899494937 Reorder the terms: -4 + v = -9.899494937 Solving -4 + v = -9.899494937 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = -9.899494937 + 4 Combine like terms: -4 + 4 = 0 0 + v = -9.899494937 + 4 v = -9.899494937 + 4 Combine like terms: -9.899494937 + 4 = -5.899494937 v = -5.899494937 Simplifying v = -5.899494937Solution
The solution to the problem is based on the solutions from the subproblems. v = {13.899494937, -5.899494937}
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