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Simplifying 10v2 + -39v + 10 = 0 Reorder the terms: 10 + -39v + 10v2 = 0 Solving 10 + -39v + 10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1 + -3.9v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.9v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + -3.9v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.9v + v2 = 0 + -1 -3.9v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.9v + v2 = -1 The v term is -3.9v. Take half its coefficient (-1.95). Square it (3.8025) and add it to both sides. Add '3.8025' to each side of the equation. -3.9v + 3.8025 + v2 = -1 + 3.8025 Reorder the terms: 3.8025 + -3.9v + v2 = -1 + 3.8025 Combine like terms: -1 + 3.8025 = 2.8025 3.8025 + -3.9v + v2 = 2.8025 Factor a perfect square on the left side: (v + -1.95)(v + -1.95) = 2.8025 Calculate the square root of the right side: 1.674066904 Break this problem into two subproblems by setting (v + -1.95) equal to 1.674066904 and -1.674066904.Subproblem 1
v + -1.95 = 1.674066904 Simplifying v + -1.95 = 1.674066904 Reorder the terms: -1.95 + v = 1.674066904 Solving -1.95 + v = 1.674066904 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + v = 1.674066904 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + v = 1.674066904 + 1.95 v = 1.674066904 + 1.95 Combine like terms: 1.674066904 + 1.95 = 3.624066904 v = 3.624066904 Simplifying v = 3.624066904Subproblem 2
v + -1.95 = -1.674066904 Simplifying v + -1.95 = -1.674066904 Reorder the terms: -1.95 + v = -1.674066904 Solving -1.95 + v = -1.674066904 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + v = -1.674066904 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + v = -1.674066904 + 1.95 v = -1.674066904 + 1.95 Combine like terms: -1.674066904 + 1.95 = 0.275933096 v = 0.275933096 Simplifying v = 0.275933096Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.624066904, 0.275933096}
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