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Simplifying (4v2 + -9v + -6) + (9v2 + 5v + 4) + -1(-7v2 + 7v + 5) = 0 Reorder the terms: (-6 + -9v + 4v2) + (9v2 + 5v + 4) + -1(-7v2 + 7v + 5) = 0 Remove parenthesis around (-6 + -9v + 4v2) -6 + -9v + 4v2 + (9v2 + 5v + 4) + -1(-7v2 + 7v + 5) = 0 Reorder the terms: -6 + -9v + 4v2 + (4 + 5v + 9v2) + -1(-7v2 + 7v + 5) = 0 Remove parenthesis around (4 + 5v + 9v2) -6 + -9v + 4v2 + 4 + 5v + 9v2 + -1(-7v2 + 7v + 5) = 0 Reorder the terms: -6 + -9v + 4v2 + 4 + 5v + 9v2 + -1(5 + 7v + -7v2) = 0 -6 + -9v + 4v2 + 4 + 5v + 9v2 + (5 * -1 + 7v * -1 + -7v2 * -1) = 0 -6 + -9v + 4v2 + 4 + 5v + 9v2 + (-5 + -7v + 7v2) = 0 Reorder the terms: -6 + 4 + -5 + -9v + 5v + -7v + 4v2 + 9v2 + 7v2 = 0 Combine like terms: -6 + 4 = -2 -2 + -5 + -9v + 5v + -7v + 4v2 + 9v2 + 7v2 = 0 Combine like terms: -2 + -5 = -7 -7 + -9v + 5v + -7v + 4v2 + 9v2 + 7v2 = 0 Combine like terms: -9v + 5v = -4v -7 + -4v + -7v + 4v2 + 9v2 + 7v2 = 0 Combine like terms: -4v + -7v = -11v -7 + -11v + 4v2 + 9v2 + 7v2 = 0 Combine like terms: 4v2 + 9v2 = 13v2 -7 + -11v + 13v2 + 7v2 = 0 Combine like terms: 13v2 + 7v2 = 20v2 -7 + -11v + 20v2 = 0 Solving -7 + -11v + 20v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.35 + -0.55v + v2 = 0.0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -0.55v + 0.35 + v2 = 0.0 + 0.35 Reorder the terms: -0.35 + 0.35 + -0.55v + v2 = 0.0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -0.55v + v2 = 0.0 + 0.35 -0.55v + v2 = 0.0 + 0.35 Combine like terms: 0.0 + 0.35 = 0.35 -0.55v + v2 = 0.35 The v term is -0.55v. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55v + 0.075625 + v2 = 0.35 + 0.075625 Reorder the terms: 0.075625 + -0.55v + v2 = 0.35 + 0.075625 Combine like terms: 0.35 + 0.075625 = 0.425625 0.075625 + -0.55v + v2 = 0.425625 Factor a perfect square on the left side: (v + -0.275)(v + -0.275) = 0.425625 Calculate the square root of the right side: 0.652399418 Break this problem into two subproblems by setting (v + -0.275) equal to 0.652399418 and -0.652399418.Subproblem 1
v + -0.275 = 0.652399418 Simplifying v + -0.275 = 0.652399418 Reorder the terms: -0.275 + v = 0.652399418 Solving -0.275 + v = 0.652399418 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + v = 0.652399418 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + v = 0.652399418 + 0.275 v = 0.652399418 + 0.275 Combine like terms: 0.652399418 + 0.275 = 0.927399418 v = 0.927399418 Simplifying v = 0.927399418Subproblem 2
v + -0.275 = -0.652399418 Simplifying v + -0.275 = -0.652399418 Reorder the terms: -0.275 + v = -0.652399418 Solving -0.275 + v = -0.652399418 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + v = -0.652399418 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + v = -0.652399418 + 0.275 v = -0.652399418 + 0.275 Combine like terms: -0.652399418 + 0.275 = -0.377399418 v = -0.377399418 Simplifying v = -0.377399418Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.927399418, -0.377399418}
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