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Simplifying 5v2 + -19v + -3 = 0 Reorder the terms: -3 + -19v + 5v2 = 0 Solving -3 + -19v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -3.8v + v2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.8v + 0.6 + v2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.8v + v2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.8v + v2 = 0 + 0.6 -3.8v + v2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3.8v + v2 = 0.6 The v term is -3.8v. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8v + 3.61 + v2 = 0.6 + 3.61 Reorder the terms: 3.61 + -3.8v + v2 = 0.6 + 3.61 Combine like terms: 0.6 + 3.61 = 4.21 3.61 + -3.8v + v2 = 4.21 Factor a perfect square on the left side: (v + -1.9)(v + -1.9) = 4.21 Calculate the square root of the right side: 2.051828453 Break this problem into two subproblems by setting (v + -1.9) equal to 2.051828453 and -2.051828453.Subproblem 1
v + -1.9 = 2.051828453 Simplifying v + -1.9 = 2.051828453 Reorder the terms: -1.9 + v = 2.051828453 Solving -1.9 + v = 2.051828453 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + v = 2.051828453 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + v = 2.051828453 + 1.9 v = 2.051828453 + 1.9 Combine like terms: 2.051828453 + 1.9 = 3.951828453 v = 3.951828453 Simplifying v = 3.951828453Subproblem 2
v + -1.9 = -2.051828453 Simplifying v + -1.9 = -2.051828453 Reorder the terms: -1.9 + v = -2.051828453 Solving -1.9 + v = -2.051828453 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + v = -2.051828453 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + v = -2.051828453 + 1.9 v = -2.051828453 + 1.9 Combine like terms: -2.051828453 + 1.9 = -0.151828453 v = -0.151828453 Simplifying v = -0.151828453Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.951828453, -0.151828453}
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