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Simplifying v2 + -1v = 43 Reorder the terms: -1v + v2 = 43 Solving -1v + v2 = 43 Solving for variable 'v'. Reorder the terms: -43 + -1v + v2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -1v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -1v + 43 + v2 = 0 + 43 Reorder the terms: -43 + 43 + -1v + v2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -1v + v2 = 0 + 43 -1v + v2 = 0 + 43 Combine like terms: 0 + 43 = 43 -1v + v2 = 43 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 43 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 43 + 0.25 Combine like terms: 43 + 0.25 = 43.25 0.25 + -1v + v2 = 43.25 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (v + -0.5) equal to 6.576473219 and -6.576473219.Subproblem 1
v + -0.5 = 6.576473219 Simplifying v + -0.5 = 6.576473219 Reorder the terms: -0.5 + v = 6.576473219 Solving -0.5 + v = 6.576473219 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 6.576473219 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 6.576473219 + 0.5 v = 6.576473219 + 0.5 Combine like terms: 6.576473219 + 0.5 = 7.076473219 v = 7.076473219 Simplifying v = 7.076473219Subproblem 2
v + -0.5 = -6.576473219 Simplifying v + -0.5 = -6.576473219 Reorder the terms: -0.5 + v = -6.576473219 Solving -0.5 + v = -6.576473219 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -6.576473219 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -6.576473219 + 0.5 v = -6.576473219 + 0.5 Combine like terms: -6.576473219 + 0.5 = -6.076473219 v = -6.076473219 Simplifying v = -6.076473219Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.076473219, -6.076473219}
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