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Simplifying (6v2 + 3v) + -1(-4v2 + -3v + 7) = 0 Reorder the terms: (3v + 6v2) + -1(-4v2 + -3v + 7) = 0 Remove parenthesis around (3v + 6v2) 3v + 6v2 + -1(-4v2 + -3v + 7) = 0 Reorder the terms: 3v + 6v2 + -1(7 + -3v + -4v2) = 0 3v + 6v2 + (7 * -1 + -3v * -1 + -4v2 * -1) = 0 3v + 6v2 + (-7 + 3v + 4v2) = 0 Reorder the terms: -7 + 3v + 3v + 6v2 + 4v2 = 0 Combine like terms: 3v + 3v = 6v -7 + 6v + 6v2 + 4v2 = 0 Combine like terms: 6v2 + 4v2 = 10v2 -7 + 6v + 10v2 = 0 Solving -7 + 6v + 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'. -0.7 + 0.6v + v2 = 0.0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.6v + 0.7 + v2 = 0.0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.6v + v2 = 0.0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.6v + v2 = 0.0 + 0.7 0.6v + v2 = 0.0 + 0.7 Combine like terms: 0.0 + 0.7 = 0.7 0.6v + v2 = 0.7 The v term is 0.6v. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6v + 0.09 + v2 = 0.7 + 0.09 Reorder the terms: 0.09 + 0.6v + v2 = 0.7 + 0.09 Combine like terms: 0.7 + 0.09 = 0.79 0.09 + 0.6v + v2 = 0.79 Factor a perfect square on the left side: (v + 0.3)(v + 0.3) = 0.79 Calculate the square root of the right side: 0.888819442 Break this problem into two subproblems by setting (v + 0.3) equal to 0.888819442 and -0.888819442.Subproblem 1
v + 0.3 = 0.888819442 Simplifying v + 0.3 = 0.888819442 Reorder the terms: 0.3 + v = 0.888819442 Solving 0.3 + v = 0.888819442 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + v = 0.888819442 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + v = 0.888819442 + -0.3 v = 0.888819442 + -0.3 Combine like terms: 0.888819442 + -0.3 = 0.588819442 v = 0.588819442 Simplifying v = 0.588819442Subproblem 2
v + 0.3 = -0.888819442 Simplifying v + 0.3 = -0.888819442 Reorder the terms: 0.3 + v = -0.888819442 Solving 0.3 + v = -0.888819442 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + v = -0.888819442 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + v = -0.888819442 + -0.3 v = -0.888819442 + -0.3 Combine like terms: -0.888819442 + -0.3 = -1.188819442 v = -1.188819442 Simplifying v = -1.188819442Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.588819442, -1.188819442}
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