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Simplifying 5v2 + -34v + -24 = 0 Reorder the terms: -24 + -34v + 5v2 = 0 Solving -24 + -34v + 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'. -4.8 + -6.8v + v2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -6.8v + 4.8 + v2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -6.8v + v2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -6.8v + v2 = 0 + 4.8 -6.8v + v2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -6.8v + v2 = 4.8 The v term is -6.8v. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8v + 11.56 + v2 = 4.8 + 11.56 Reorder the terms: 11.56 + -6.8v + v2 = 4.8 + 11.56 Combine like terms: 4.8 + 11.56 = 16.36 11.56 + -6.8v + v2 = 16.36 Factor a perfect square on the left side: (v + -3.4)(v + -3.4) = 16.36 Calculate the square root of the right side: 4.044749683 Break this problem into two subproblems by setting (v + -3.4) equal to 4.044749683 and -4.044749683.Subproblem 1
v + -3.4 = 4.044749683 Simplifying v + -3.4 = 4.044749683 Reorder the terms: -3.4 + v = 4.044749683 Solving -3.4 + v = 4.044749683 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + v = 4.044749683 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + v = 4.044749683 + 3.4 v = 4.044749683 + 3.4 Combine like terms: 4.044749683 + 3.4 = 7.444749683 v = 7.444749683 Simplifying v = 7.444749683Subproblem 2
v + -3.4 = -4.044749683 Simplifying v + -3.4 = -4.044749683 Reorder the terms: -3.4 + v = -4.044749683 Solving -3.4 + v = -4.044749683 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + v = -4.044749683 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + v = -4.044749683 + 3.4 v = -4.044749683 + 3.4 Combine like terms: -4.044749683 + 3.4 = -0.644749683 v = -0.644749683 Simplifying v = -0.644749683Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.444749683, -0.644749683}
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