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Simplifying (3v2 + 9v) + -1(-7v2 + -4v + 4) = 0 Reorder the terms: (9v + 3v2) + -1(-7v2 + -4v + 4) = 0 Remove parenthesis around (9v + 3v2) 9v + 3v2 + -1(-7v2 + -4v + 4) = 0 Reorder the terms: 9v + 3v2 + -1(4 + -4v + -7v2) = 0 9v + 3v2 + (4 * -1 + -4v * -1 + -7v2 * -1) = 0 9v + 3v2 + (-4 + 4v + 7v2) = 0 Reorder the terms: -4 + 9v + 4v + 3v2 + 7v2 = 0 Combine like terms: 9v + 4v = 13v -4 + 13v + 3v2 + 7v2 = 0 Combine like terms: 3v2 + 7v2 = 10v2 -4 + 13v + 10v2 = 0 Solving -4 + 13v + 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'. -0.4 + 1.3v + v2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.3v + 0.4 + v2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.3v + v2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.3v + v2 = 0.0 + 0.4 1.3v + v2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 1.3v + v2 = 0.4 The v term is 1.3v. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3v + 0.4225 + v2 = 0.4 + 0.4225 Reorder the terms: 0.4225 + 1.3v + v2 = 0.4 + 0.4225 Combine like terms: 0.4 + 0.4225 = 0.8225 0.4225 + 1.3v + v2 = 0.8225 Factor a perfect square on the left side: (v + 0.65)(v + 0.65) = 0.8225 Calculate the square root of the right side: 0.906917857 Break this problem into two subproblems by setting (v + 0.65) equal to 0.906917857 and -0.906917857.Subproblem 1
v + 0.65 = 0.906917857 Simplifying v + 0.65 = 0.906917857 Reorder the terms: 0.65 + v = 0.906917857 Solving 0.65 + v = 0.906917857 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + v = 0.906917857 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + v = 0.906917857 + -0.65 v = 0.906917857 + -0.65 Combine like terms: 0.906917857 + -0.65 = 0.256917857 v = 0.256917857 Simplifying v = 0.256917857Subproblem 2
v + 0.65 = -0.906917857 Simplifying v + 0.65 = -0.906917857 Reorder the terms: 0.65 + v = -0.906917857 Solving 0.65 + v = -0.906917857 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + v = -0.906917857 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + v = -0.906917857 + -0.65 v = -0.906917857 + -0.65 Combine like terms: -0.906917857 + -0.65 = -1.556917857 v = -1.556917857 Simplifying v = -1.556917857Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.256917857, -1.556917857}
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