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Simplifying 2v2 + 105v + 90 = 0 Reorder the terms: 90 + 105v + 2v2 = 0 Solving 90 + 105v + 2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 45 + 52.5v + v2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + 52.5v + -45 + v2 = 0 + -45 Reorder the terms: 45 + -45 + 52.5v + v2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 52.5v + v2 = 0 + -45 52.5v + v2 = 0 + -45 Combine like terms: 0 + -45 = -45 52.5v + v2 = -45 The v term is 52.5v. Take half its coefficient (26.25). Square it (689.0625) and add it to both sides. Add '689.0625' to each side of the equation. 52.5v + 689.0625 + v2 = -45 + 689.0625 Reorder the terms: 689.0625 + 52.5v + v2 = -45 + 689.0625 Combine like terms: -45 + 689.0625 = 644.0625 689.0625 + 52.5v + v2 = 644.0625 Factor a perfect square on the left side: (v + 26.25)(v + 26.25) = 644.0625 Calculate the square root of the right side: 25.378386474 Break this problem into two subproblems by setting (v + 26.25) equal to 25.378386474 and -25.378386474.Subproblem 1
v + 26.25 = 25.378386474 Simplifying v + 26.25 = 25.378386474 Reorder the terms: 26.25 + v = 25.378386474 Solving 26.25 + v = 25.378386474 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-26.25' to each side of the equation. 26.25 + -26.25 + v = 25.378386474 + -26.25 Combine like terms: 26.25 + -26.25 = 0.00 0.00 + v = 25.378386474 + -26.25 v = 25.378386474 + -26.25 Combine like terms: 25.378386474 + -26.25 = -0.871613526 v = -0.871613526 Simplifying v = -0.871613526Subproblem 2
v + 26.25 = -25.378386474 Simplifying v + 26.25 = -25.378386474 Reorder the terms: 26.25 + v = -25.378386474 Solving 26.25 + v = -25.378386474 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-26.25' to each side of the equation. 26.25 + -26.25 + v = -25.378386474 + -26.25 Combine like terms: 26.25 + -26.25 = 0.00 0.00 + v = -25.378386474 + -26.25 v = -25.378386474 + -26.25 Combine like terms: -25.378386474 + -26.25 = -51.628386474 v = -51.628386474 Simplifying v = -51.628386474Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.871613526, -51.628386474}
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