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Simplifying 26 = -0.0088v2 + 0.75v + 14 Reorder the terms: 26 = 14 + 0.75v + -0.0088v2 Solving 26 = 14 + 0.75v + -0.0088v2 Solving for variable 'v'. Combine like terms: 26 + -14 = 12 12 + -0.75v + 0.0088v2 = 14 + 0.75v + -0.0088v2 + -14 + -0.75v + 0.0088v2 Reorder the terms: 12 + -0.75v + 0.0088v2 = 14 + -14 + 0.75v + -0.75v + -0.0088v2 + 0.0088v2 Combine like terms: 14 + -14 = 0 12 + -0.75v + 0.0088v2 = 0 + 0.75v + -0.75v + -0.0088v2 + 0.0088v2 12 + -0.75v + 0.0088v2 = 0.75v + -0.75v + -0.0088v2 + 0.0088v2 Combine like terms: 0.75v + -0.75v = 0.00 12 + -0.75v + 0.0088v2 = 0.00 + -0.0088v2 + 0.0088v2 12 + -0.75v + 0.0088v2 = -0.0088v2 + 0.0088v2 Combine like terms: -0.0088v2 + 0.0088v2 = 0.0000 12 + -0.75v + 0.0088v2 = 0.0000 Begin completing the square. Divide all terms by 0.0088 the coefficient of the squared term: Divide each side by '0.0088'. 1363.636364 + -85.22727273v + v2 = 0 Move the constant term to the right: Add '-1363.636364' to each side of the equation. 1363.636364 + -85.22727273v + -1363.636364 + v2 = 0 + -1363.636364 Reorder the terms: 1363.636364 + -1363.636364 + -85.22727273v + v2 = 0 + -1363.636364 Combine like terms: 1363.636364 + -1363.636364 = 0.000000 0.000000 + -85.22727273v + v2 = 0 + -1363.636364 -85.22727273v + v2 = 0 + -1363.636364 Combine like terms: 0 + -1363.636364 = -1363.636364 -85.22727273v + v2 = -1363.636364 The v term is -85.22727273v. Take half its coefficient (-42.61363637). Square it (1815.922005) and add it to both sides. Add '1815.922005' to each side of the equation. -85.22727273v + 1815.922005 + v2 = -1363.636364 + 1815.922005 Reorder the terms: 1815.922005 + -85.22727273v + v2 = -1363.636364 + 1815.922005 Combine like terms: -1363.636364 + 1815.922005 = 452.285641 1815.922005 + -85.22727273v + v2 = 452.285641 Factor a perfect square on the left side: (v + -42.61363637)(v + -42.61363637) = 452.285641 Calculate the square root of the right side: 21.267008276 Break this problem into two subproblems by setting (v + -42.61363637) equal to 21.267008276 and -21.267008276.Subproblem 1
v + -42.61363637 = 21.267008276 Simplifying v + -42.61363637 = 21.267008276 Reorder the terms: -42.61363637 + v = 21.267008276 Solving -42.61363637 + v = 21.267008276 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '42.61363637' to each side of the equation. -42.61363637 + 42.61363637 + v = 21.267008276 + 42.61363637 Combine like terms: -42.61363637 + 42.61363637 = 0.00000000 0.00000000 + v = 21.267008276 + 42.61363637 v = 21.267008276 + 42.61363637 Combine like terms: 21.267008276 + 42.61363637 = 63.880644646 v = 63.880644646 Simplifying v = 63.880644646Subproblem 2
v + -42.61363637 = -21.267008276 Simplifying v + -42.61363637 = -21.267008276 Reorder the terms: -42.61363637 + v = -21.267008276 Solving -42.61363637 + v = -21.267008276 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '42.61363637' to each side of the equation. -42.61363637 + 42.61363637 + v = -21.267008276 + 42.61363637 Combine like terms: -42.61363637 + 42.61363637 = 0.00000000 0.00000000 + v = -21.267008276 + 42.61363637 v = -21.267008276 + 42.61363637 Combine like terms: -21.267008276 + 42.61363637 = 21.346628094 v = 21.346628094 Simplifying v = 21.346628094Solution
The solution to the problem is based on the solutions from the subproblems. v = {63.880644646, 21.346628094}
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