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Simplifying (5v2 + -4v + -4) + (9v2 + -5v + -1) + -1(-7v2 + 4v + 7) = 0 Reorder the terms: (-4 + -4v + 5v2) + (9v2 + -5v + -1) + -1(-7v2 + 4v + 7) = 0 Remove parenthesis around (-4 + -4v + 5v2) -4 + -4v + 5v2 + (9v2 + -5v + -1) + -1(-7v2 + 4v + 7) = 0 Reorder the terms: -4 + -4v + 5v2 + (-1 + -5v + 9v2) + -1(-7v2 + 4v + 7) = 0 Remove parenthesis around (-1 + -5v + 9v2) -4 + -4v + 5v2 + -1 + -5v + 9v2 + -1(-7v2 + 4v + 7) = 0 Reorder the terms: -4 + -4v + 5v2 + -1 + -5v + 9v2 + -1(7 + 4v + -7v2) = 0 -4 + -4v + 5v2 + -1 + -5v + 9v2 + (7 * -1 + 4v * -1 + -7v2 * -1) = 0 -4 + -4v + 5v2 + -1 + -5v + 9v2 + (-7 + -4v + 7v2) = 0 Reorder the terms: -4 + -1 + -7 + -4v + -5v + -4v + 5v2 + 9v2 + 7v2 = 0 Combine like terms: -4 + -1 = -5 -5 + -7 + -4v + -5v + -4v + 5v2 + 9v2 + 7v2 = 0 Combine like terms: -5 + -7 = -12 -12 + -4v + -5v + -4v + 5v2 + 9v2 + 7v2 = 0 Combine like terms: -4v + -5v = -9v -12 + -9v + -4v + 5v2 + 9v2 + 7v2 = 0 Combine like terms: -9v + -4v = -13v -12 + -13v + 5v2 + 9v2 + 7v2 = 0 Combine like terms: 5v2 + 9v2 = 14v2 -12 + -13v + 14v2 + 7v2 = 0 Combine like terms: 14v2 + 7v2 = 21v2 -12 + -13v + 21v2 = 0 Solving -12 + -13v + 21v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.5714285714 + -0.619047619v + v2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.619047619v + 0.5714285714 + v2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.619047619v + v2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.619047619v + v2 = 0 + 0.5714285714 -0.619047619v + v2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.619047619v + v2 = 0.5714285714 The v term is -0.619047619v. Take half its coefficient (-0.3095238095). Square it (0.09580498865) and add it to both sides. Add '0.09580498865' to each side of the equation. -0.619047619v + 0.09580498865 + v2 = 0.5714285714 + 0.09580498865 Reorder the terms: 0.09580498865 + -0.619047619v + v2 = 0.5714285714 + 0.09580498865 Combine like terms: 0.5714285714 + 0.09580498865 = 0.66723356005 0.09580498865 + -0.619047619v + v2 = 0.66723356005 Factor a perfect square on the left side: (v + -0.3095238095)(v + -0.3095238095) = 0.66723356005 Calculate the square root of the right side: 0.816843657 Break this problem into two subproblems by setting (v + -0.3095238095) equal to 0.816843657 and -0.816843657.Subproblem 1
v + -0.3095238095 = 0.816843657 Simplifying v + -0.3095238095 = 0.816843657 Reorder the terms: -0.3095238095 + v = 0.816843657 Solving -0.3095238095 + v = 0.816843657 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3095238095' to each side of the equation. -0.3095238095 + 0.3095238095 + v = 0.816843657 + 0.3095238095 Combine like terms: -0.3095238095 + 0.3095238095 = 0.0000000000 0.0000000000 + v = 0.816843657 + 0.3095238095 v = 0.816843657 + 0.3095238095 Combine like terms: 0.816843657 + 0.3095238095 = 1.1263674665 v = 1.1263674665 Simplifying v = 1.1263674665Subproblem 2
v + -0.3095238095 = -0.816843657 Simplifying v + -0.3095238095 = -0.816843657 Reorder the terms: -0.3095238095 + v = -0.816843657 Solving -0.3095238095 + v = -0.816843657 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3095238095' to each side of the equation. -0.3095238095 + 0.3095238095 + v = -0.816843657 + 0.3095238095 Combine like terms: -0.3095238095 + 0.3095238095 = 0.0000000000 0.0000000000 + v = -0.816843657 + 0.3095238095 v = -0.816843657 + 0.3095238095 Combine like terms: -0.816843657 + 0.3095238095 = -0.5073198475 v = -0.5073198475 Simplifying v = -0.5073198475Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.1263674665, -0.5073198475}
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