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Simplifying 5v2 + 39v + -32 = 0 Reorder the terms: -32 + 39v + 5v2 = 0 Solving -32 + 39v + 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'. -6.4 + 7.8v + v2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 7.8v + 6.4 + v2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 7.8v + v2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 7.8v + v2 = 0 + 6.4 7.8v + v2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 7.8v + v2 = 6.4 The v term is 7.8v. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8v + 15.21 + v2 = 6.4 + 15.21 Reorder the terms: 15.21 + 7.8v + v2 = 6.4 + 15.21 Combine like terms: 6.4 + 15.21 = 21.61 15.21 + 7.8v + v2 = 21.61 Factor a perfect square on the left side: (v + 3.9)(v + 3.9) = 21.61 Calculate the square root of the right side: 4.64865572 Break this problem into two subproblems by setting (v + 3.9) equal to 4.64865572 and -4.64865572.Subproblem 1
v + 3.9 = 4.64865572 Simplifying v + 3.9 = 4.64865572 Reorder the terms: 3.9 + v = 4.64865572 Solving 3.9 + v = 4.64865572 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + v = 4.64865572 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + v = 4.64865572 + -3.9 v = 4.64865572 + -3.9 Combine like terms: 4.64865572 + -3.9 = 0.74865572 v = 0.74865572 Simplifying v = 0.74865572Subproblem 2
v + 3.9 = -4.64865572 Simplifying v + 3.9 = -4.64865572 Reorder the terms: 3.9 + v = -4.64865572 Solving 3.9 + v = -4.64865572 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + v = -4.64865572 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + v = -4.64865572 + -3.9 v = -4.64865572 + -3.9 Combine like terms: -4.64865572 + -3.9 = -8.54865572 v = -8.54865572 Simplifying v = -8.54865572Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.74865572, -8.54865572}
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