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Simplifying -1v2 + 1v + 24 = 0 Reorder the terms: 24 + 1v + -1v2 = 0 Solving 24 + 1v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -1v + v2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -1v + 24 + v2 = 0 + 24 Reorder the terms: -24 + 24 + -1v + v2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1v + v2 = 0 + 24 -1v + v2 = 0 + 24 Combine like terms: 0 + 24 = 24 -1v + v2 = 24 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 = 24 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 24 + 0.25 Combine like terms: 24 + 0.25 = 24.25 0.25 + -1v + v2 = 24.25 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (v + -0.5) equal to 4.924428901 and -4.924428901.Subproblem 1
v + -0.5 = 4.924428901 Simplifying v + -0.5 = 4.924428901 Reorder the terms: -0.5 + v = 4.924428901 Solving -0.5 + v = 4.924428901 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 = 4.924428901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 4.924428901 + 0.5 v = 4.924428901 + 0.5 Combine like terms: 4.924428901 + 0.5 = 5.424428901 v = 5.424428901 Simplifying v = 5.424428901Subproblem 2
v + -0.5 = -4.924428901 Simplifying v + -0.5 = -4.924428901 Reorder the terms: -0.5 + v = -4.924428901 Solving -0.5 + v = -4.924428901 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 = -4.924428901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -4.924428901 + 0.5 v = -4.924428901 + 0.5 Combine like terms: -4.924428901 + 0.5 = -4.424428901 v = -4.424428901 Simplifying v = -4.424428901Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.424428901, -4.424428901}
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