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Simplifying (-2v2 + 7v + -4) + -1(-3v2 + 9v + -3) + (-2v2 + -5v + 3) = 0 Reorder the terms: (-4 + 7v + -2v2) + -1(-3v2 + 9v + -3) + (-2v2 + -5v + 3) = 0 Remove parenthesis around (-4 + 7v + -2v2) -4 + 7v + -2v2 + -1(-3v2 + 9v + -3) + (-2v2 + -5v + 3) = 0 Reorder the terms: -4 + 7v + -2v2 + -1(-3 + 9v + -3v2) + (-2v2 + -5v + 3) = 0 -4 + 7v + -2v2 + (-3 * -1 + 9v * -1 + -3v2 * -1) + (-2v2 + -5v + 3) = 0 -4 + 7v + -2v2 + (3 + -9v + 3v2) + (-2v2 + -5v + 3) = 0 Reorder the terms: -4 + 7v + -2v2 + 3 + -9v + 3v2 + (3 + -5v + -2v2) = 0 Remove parenthesis around (3 + -5v + -2v2) -4 + 7v + -2v2 + 3 + -9v + 3v2 + 3 + -5v + -2v2 = 0 Reorder the terms: -4 + 3 + 3 + 7v + -9v + -5v + -2v2 + 3v2 + -2v2 = 0 Combine like terms: -4 + 3 = -1 -1 + 3 + 7v + -9v + -5v + -2v2 + 3v2 + -2v2 = 0 Combine like terms: -1 + 3 = 2 2 + 7v + -9v + -5v + -2v2 + 3v2 + -2v2 = 0 Combine like terms: 7v + -9v = -2v 2 + -2v + -5v + -2v2 + 3v2 + -2v2 = 0 Combine like terms: -2v + -5v = -7v 2 + -7v + -2v2 + 3v2 + -2v2 = 0 Combine like terms: -2v2 + 3v2 = 1v2 2 + -7v + 1v2 + -2v2 = 0 Combine like terms: 1v2 + -2v2 = -1v2 2 + -7v + -1v2 = 0 Solving 2 + -7v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 7v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 7v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 7v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7v + v2 = 0 + 2 7v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 7v + v2 = 2 The v term is 7v. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7v + 12.25 + v2 = 2 + 12.25 Reorder the terms: 12.25 + 7v + v2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + 7v + v2 = 14.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (v + 3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
v + 3.5 = 3.774917218 Simplifying v + 3.5 = 3.774917218 Reorder the terms: 3.5 + v = 3.774917218 Solving 3.5 + v = 3.774917218 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = 3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 3.774917218 + -3.5 v = 3.774917218 + -3.5 Combine like terms: 3.774917218 + -3.5 = 0.274917218 v = 0.274917218 Simplifying v = 0.274917218Subproblem 2
v + 3.5 = -3.774917218 Simplifying v + 3.5 = -3.774917218 Reorder the terms: 3.5 + v = -3.774917218 Solving 3.5 + v = -3.774917218 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = -3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -3.774917218 + -3.5 v = -3.774917218 + -3.5 Combine like terms: -3.774917218 + -3.5 = -7.274917218 v = -7.274917218 Simplifying v = -7.274917218Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.274917218, -7.274917218}
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