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Simplifying 9v2 + -25 = 9v Reorder the terms: -25 + 9v2 = 9v Solving -25 + 9v2 = 9v Solving for variable 'v'. Reorder the terms: -25 + -9v + 9v2 = 9v + -9v Combine like terms: 9v + -9v = 0 -25 + -9v + 9v2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.777777778 + -1v + v2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -1v + 2.777777778 + v2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -1v + v2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -1v + v2 = 0 + 2.777777778 -1v + v2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -1v + v2 = 2.777777778 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 = 2.777777778 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 2.777777778 + 0.25 Combine like terms: 2.777777778 + 0.25 = 3.027777778 0.25 + -1v + v2 = 3.027777778 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 3.027777778 Calculate the square root of the right side: 1.740051085 Break this problem into two subproblems by setting (v + -0.5) equal to 1.740051085 and -1.740051085.Subproblem 1
v + -0.5 = 1.740051085 Simplifying v + -0.5 = 1.740051085 Reorder the terms: -0.5 + v = 1.740051085 Solving -0.5 + v = 1.740051085 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 = 1.740051085 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 1.740051085 + 0.5 v = 1.740051085 + 0.5 Combine like terms: 1.740051085 + 0.5 = 2.240051085 v = 2.240051085 Simplifying v = 2.240051085Subproblem 2
v + -0.5 = -1.740051085 Simplifying v + -0.5 = -1.740051085 Reorder the terms: -0.5 + v = -1.740051085 Solving -0.5 + v = -1.740051085 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 = -1.740051085 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -1.740051085 + 0.5 v = -1.740051085 + 0.5 Combine like terms: -1.740051085 + 0.5 = -1.240051085 v = -1.240051085 Simplifying v = -1.240051085Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.240051085, -1.240051085}
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