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Simplifying 10v2 + 9v + -2 = 0 Reorder the terms: -2 + 9v + 10v2 = 0 Solving -2 + 9v + 10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + 0.9v + v2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.9v + 0.2 + v2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.9v + v2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.9v + v2 = 0 + 0.2 0.9v + v2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.9v + v2 = 0.2 The v term is 0.9v. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9v + 0.2025 + v2 = 0.2 + 0.2025 Reorder the terms: 0.2025 + 0.9v + v2 = 0.2 + 0.2025 Combine like terms: 0.2 + 0.2025 = 0.4025 0.2025 + 0.9v + v2 = 0.4025 Factor a perfect square on the left side: (v + 0.45)(v + 0.45) = 0.4025 Calculate the square root of the right side: 0.634428877 Break this problem into two subproblems by setting (v + 0.45) equal to 0.634428877 and -0.634428877.Subproblem 1
v + 0.45 = 0.634428877 Simplifying v + 0.45 = 0.634428877 Reorder the terms: 0.45 + v = 0.634428877 Solving 0.45 + v = 0.634428877 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + v = 0.634428877 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + v = 0.634428877 + -0.45 v = 0.634428877 + -0.45 Combine like terms: 0.634428877 + -0.45 = 0.184428877 v = 0.184428877 Simplifying v = 0.184428877Subproblem 2
v + 0.45 = -0.634428877 Simplifying v + 0.45 = -0.634428877 Reorder the terms: 0.45 + v = -0.634428877 Solving 0.45 + v = -0.634428877 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + v = -0.634428877 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + v = -0.634428877 + -0.45 v = -0.634428877 + -0.45 Combine like terms: -0.634428877 + -0.45 = -1.084428877 v = -1.084428877 Simplifying v = -1.084428877Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.184428877, -1.084428877}
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