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Simplifying 3v2 + 2v + -75 = 0 Reorder the terms: -75 + 2v + 3v2 = 0 Solving -75 + 2v + 3v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25 + 0.6666666667v + v2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.6666666667v + 25 + v2 = 0 + 25 Reorder the terms: -25 + 25 + 0.6666666667v + v2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.6666666667v + v2 = 0 + 25 0.6666666667v + v2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.6666666667v + v2 = 25 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 = 25 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667v + v2 = 25 + 0.1111111112 Combine like terms: 25 + 0.1111111112 = 25.1111111112 0.1111111112 + 0.6666666667v + v2 = 25.1111111112 Factor a perfect square on the left side: (v + 0.3333333334)(v + 0.3333333334) = 25.1111111112 Calculate the square root of the right side: 5.011098793 Break this problem into two subproblems by setting (v + 0.3333333334) equal to 5.011098793 and -5.011098793.Subproblem 1
v + 0.3333333334 = 5.011098793 Simplifying v + 0.3333333334 = 5.011098793 Reorder the terms: 0.3333333334 + v = 5.011098793 Solving 0.3333333334 + v = 5.011098793 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 = 5.011098793 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + v = 5.011098793 + -0.3333333334 v = 5.011098793 + -0.3333333334 Combine like terms: 5.011098793 + -0.3333333334 = 4.6777654596 v = 4.6777654596 Simplifying v = 4.6777654596Subproblem 2
v + 0.3333333334 = -5.011098793 Simplifying v + 0.3333333334 = -5.011098793 Reorder the terms: 0.3333333334 + v = -5.011098793 Solving 0.3333333334 + v = -5.011098793 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 = -5.011098793 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + v = -5.011098793 + -0.3333333334 v = -5.011098793 + -0.3333333334 Combine like terms: -5.011098793 + -0.3333333334 = -5.3444321264 v = -5.3444321264 Simplifying v = -5.3444321264Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.6777654596, -5.3444321264}
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