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Simplifying 5v2 + -22v + 13 = 0 Reorder the terms: 13 + -22v + 5v2 = 0 Solving 13 + -22v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.6 + -4.4v + v2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -4.4v + -2.6 + v2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -4.4v + v2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -4.4v + v2 = 0 + -2.6 -4.4v + v2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -4.4v + v2 = -2.6 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 = -2.6 + 4.84 Reorder the terms: 4.84 + -4.4v + v2 = -2.6 + 4.84 Combine like terms: -2.6 + 4.84 = 2.24 4.84 + -4.4v + v2 = 2.24 Factor a perfect square on the left side: (v + -2.2)(v + -2.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (v + -2.2) equal to 1.496662955 and -1.496662955.Subproblem 1
v + -2.2 = 1.496662955 Simplifying v + -2.2 = 1.496662955 Reorder the terms: -2.2 + v = 1.496662955 Solving -2.2 + v = 1.496662955 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 = 1.496662955 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + v = 1.496662955 + 2.2 v = 1.496662955 + 2.2 Combine like terms: 1.496662955 + 2.2 = 3.696662955 v = 3.696662955 Simplifying v = 3.696662955Subproblem 2
v + -2.2 = -1.496662955 Simplifying v + -2.2 = -1.496662955 Reorder the terms: -2.2 + v = -1.496662955 Solving -2.2 + v = -1.496662955 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 = -1.496662955 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + v = -1.496662955 + 2.2 v = -1.496662955 + 2.2 Combine like terms: -1.496662955 + 2.2 = 0.703337045 v = 0.703337045 Simplifying v = 0.703337045Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.696662955, 0.703337045}
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