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Simplifying -63 + -2v = -5v2 + 5v + -7 Reorder the terms: -63 + -2v = -7 + 5v + -5v2 Solving -63 + -2v = -7 + 5v + -5v2 Solving for variable 'v'. Reorder the terms: -63 + 7 + -2v + -5v + 5v2 = -7 + 5v + -5v2 + 7 + -5v + 5v2 Combine like terms: -63 + 7 = -56 -56 + -2v + -5v + 5v2 = -7 + 5v + -5v2 + 7 + -5v + 5v2 Combine like terms: -2v + -5v = -7v -56 + -7v + 5v2 = -7 + 5v + -5v2 + 7 + -5v + 5v2 Reorder the terms: -56 + -7v + 5v2 = -7 + 7 + 5v + -5v + -5v2 + 5v2 Combine like terms: -7 + 7 = 0 -56 + -7v + 5v2 = 0 + 5v + -5v + -5v2 + 5v2 -56 + -7v + 5v2 = 5v + -5v + -5v2 + 5v2 Combine like terms: 5v + -5v = 0 -56 + -7v + 5v2 = 0 + -5v2 + 5v2 -56 + -7v + 5v2 = -5v2 + 5v2 Combine like terms: -5v2 + 5v2 = 0 -56 + -7v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11.2 + -1.4v + v2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -1.4v + 11.2 + v2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -1.4v + v2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -1.4v + v2 = 0 + 11.2 -1.4v + v2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -1.4v + v2 = 11.2 The v term is -1.4v. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4v + 0.49 + v2 = 11.2 + 0.49 Reorder the terms: 0.49 + -1.4v + v2 = 11.2 + 0.49 Combine like terms: 11.2 + 0.49 = 11.69 0.49 + -1.4v + v2 = 11.69 Factor a perfect square on the left side: (v + -0.7)(v + -0.7) = 11.69 Calculate the square root of the right side: 3.419064199 Break this problem into two subproblems by setting (v + -0.7) equal to 3.419064199 and -3.419064199.Subproblem 1
v + -0.7 = 3.419064199 Simplifying v + -0.7 = 3.419064199 Reorder the terms: -0.7 + v = 3.419064199 Solving -0.7 + v = 3.419064199 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + v = 3.419064199 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + v = 3.419064199 + 0.7 v = 3.419064199 + 0.7 Combine like terms: 3.419064199 + 0.7 = 4.119064199 v = 4.119064199 Simplifying v = 4.119064199Subproblem 2
v + -0.7 = -3.419064199 Simplifying v + -0.7 = -3.419064199 Reorder the terms: -0.7 + v = -3.419064199 Solving -0.7 + v = -3.419064199 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + v = -3.419064199 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + v = -3.419064199 + 0.7 v = -3.419064199 + 0.7 Combine like terms: -3.419064199 + 0.7 = -2.719064199 v = -2.719064199 Simplifying v = -2.719064199Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.119064199, -2.719064199}
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