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Simplifying 10v2 + -44v + 35 = 0 Reorder the terms: 35 + -44v + 10v2 = 0 Solving 35 + -44v + 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'. 3.5 + -4.4v + v2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -4.4v + -3.5 + v2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -4.4v + v2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -4.4v + v2 = 0 + -3.5 -4.4v + v2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -4.4v + v2 = -3.5 The v term is -4.4v. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4v + 4.84 + v2 = -3.5 + 4.84 Reorder the terms: 4.84 + -4.4v + v2 = -3.5 + 4.84 Combine like terms: -3.5 + 4.84 = 1.34 4.84 + -4.4v + v2 = 1.34 Factor a perfect square on the left side: (v + -2.2)(v + -2.2) = 1.34 Calculate the square root of the right side: 1.15758369 Break this problem into two subproblems by setting (v + -2.2) equal to 1.15758369 and -1.15758369.Subproblem 1
v + -2.2 = 1.15758369 Simplifying v + -2.2 = 1.15758369 Reorder the terms: -2.2 + v = 1.15758369 Solving -2.2 + v = 1.15758369 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + v = 1.15758369 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + v = 1.15758369 + 2.2 v = 1.15758369 + 2.2 Combine like terms: 1.15758369 + 2.2 = 3.35758369 v = 3.35758369 Simplifying v = 3.35758369Subproblem 2
v + -2.2 = -1.15758369 Simplifying v + -2.2 = -1.15758369 Reorder the terms: -2.2 + v = -1.15758369 Solving -2.2 + v = -1.15758369 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + v = -1.15758369 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + v = -1.15758369 + 2.2 v = -1.15758369 + 2.2 Combine like terms: -1.15758369 + 2.2 = 1.04241631 v = 1.04241631 Simplifying v = 1.04241631Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.35758369, 1.04241631}
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