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Simplifying 9v2 + 6v + -2 = 7 Reorder the terms: -2 + 6v + 9v2 = 7 Solving -2 + 6v + 9v2 = 7 Solving for variable 'v'. Reorder the terms: -2 + -7 + 6v + 9v2 = 7 + -7 Combine like terms: -2 + -7 = -9 -9 + 6v + 9v2 = 7 + -7 Combine like terms: 7 + -7 = 0 -9 + 6v + 9v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 2v + 3v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 2v + 3v2)' equal to zero and attempt to solve: Simplifying -3 + 2v + 3v2 = 0 Solving -3 + 2v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 0.6666666667v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.6666666667v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + 0.6666666667v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.6666666667v + v2 = 0 + 1 0.6666666667v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.6666666667v + v2 = 1 The v term is 0.6666666667v. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667v + 0.1111111112 + v2 = 1 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667v + v2 = 1 + 0.1111111112 Combine like terms: 1 + 0.1111111112 = 1.1111111112 0.1111111112 + 0.6666666667v + v2 = 1.1111111112 Factor a perfect square on the left side: (v + 0.3333333334)(v + 0.3333333334) = 1.1111111112 Calculate the square root of the right side: 1.054092553 Break this problem into two subproblems by setting (v + 0.3333333334) equal to 1.054092553 and -1.054092553.Subproblem 1
v + 0.3333333334 = 1.054092553 Simplifying v + 0.3333333334 = 1.054092553 Reorder the terms: 0.3333333334 + v = 1.054092553 Solving 0.3333333334 + v = 1.054092553 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + v = 1.054092553 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + v = 1.054092553 + -0.3333333334 v = 1.054092553 + -0.3333333334 Combine like terms: 1.054092553 + -0.3333333334 = 0.7207592196 v = 0.7207592196 Simplifying v = 0.7207592196Subproblem 2
v + 0.3333333334 = -1.054092553 Simplifying v + 0.3333333334 = -1.054092553 Reorder the terms: 0.3333333334 + v = -1.054092553 Solving 0.3333333334 + v = -1.054092553 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + v = -1.054092553 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + v = -1.054092553 + -0.3333333334 v = -1.054092553 + -0.3333333334 Combine like terms: -1.054092553 + -0.3333333334 = -1.3874258864 v = -1.3874258864 Simplifying v = -1.3874258864Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.7207592196, -1.3874258864}Solution
v = {0.7207592196, -1.3874258864}
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