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Simplifying 9 = v(v + -9) Reorder the terms: 9 = v(-9 + v) 9 = (-9 * v + v * v) 9 = (-9v + v2) Solving 9 = -9v + v2 Solving for variable 'v'. Reorder the terms: 9 + 9v + -1v2 = -9v + 9v + v2 + -1v2 Combine like terms: -9v + 9v = 0 9 + 9v + -1v2 = 0 + v2 + -1v2 9 + 9v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 9 + 9v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -9v + v2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -9v + 9 + v2 = 0 + 9 Reorder the terms: -9 + 9 + -9v + v2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9v + v2 = 0 + 9 -9v + v2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9v + v2 = 9 The v term is -9v. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9v + 20.25 + v2 = 9 + 20.25 Reorder the terms: 20.25 + -9v + v2 = 9 + 20.25 Combine like terms: 9 + 20.25 = 29.25 20.25 + -9v + v2 = 29.25 Factor a perfect square on the left side: (v + -4.5)(v + -4.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (v + -4.5) equal to 5.408326913 and -5.408326913.Subproblem 1
v + -4.5 = 5.408326913 Simplifying v + -4.5 = 5.408326913 Reorder the terms: -4.5 + v = 5.408326913 Solving -4.5 + v = 5.408326913 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = 5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = 5.408326913 + 4.5 v = 5.408326913 + 4.5 Combine like terms: 5.408326913 + 4.5 = 9.908326913 v = 9.908326913 Simplifying v = 9.908326913Subproblem 2
v + -4.5 = -5.408326913 Simplifying v + -4.5 = -5.408326913 Reorder the terms: -4.5 + v = -5.408326913 Solving -4.5 + v = -5.408326913 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + v = -5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + v = -5.408326913 + 4.5 v = -5.408326913 + 4.5 Combine like terms: -5.408326913 + 4.5 = -0.908326913 v = -0.908326913 Simplifying v = -0.908326913Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.908326913, -0.908326913}
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