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Simplifying 5v2 + 28v + 20 = 0 Reorder the terms: 20 + 28v + 5v2 = 0 Solving 20 + 28v + 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 + 5.6v + v2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 5.6v + -4 + v2 = 0 + -4 Reorder the terms: 4 + -4 + 5.6v + v2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5.6v + v2 = 0 + -4 5.6v + v2 = 0 + -4 Combine like terms: 0 + -4 = -4 5.6v + v2 = -4 The v term is 5.6v. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6v + 7.84 + v2 = -4 + 7.84 Reorder the terms: 7.84 + 5.6v + v2 = -4 + 7.84 Combine like terms: -4 + 7.84 = 3.84 7.84 + 5.6v + v2 = 3.84 Factor a perfect square on the left side: (v + 2.8)(v + 2.8) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (v + 2.8) equal to 1.959591794 and -1.959591794.Subproblem 1
v + 2.8 = 1.959591794 Simplifying v + 2.8 = 1.959591794 Reorder the terms: 2.8 + v = 1.959591794 Solving 2.8 + v = 1.959591794 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + v = 1.959591794 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + v = 1.959591794 + -2.8 v = 1.959591794 + -2.8 Combine like terms: 1.959591794 + -2.8 = -0.840408206 v = -0.840408206 Simplifying v = -0.840408206Subproblem 2
v + 2.8 = -1.959591794 Simplifying v + 2.8 = -1.959591794 Reorder the terms: 2.8 + v = -1.959591794 Solving 2.8 + v = -1.959591794 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + v = -1.959591794 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + v = -1.959591794 + -2.8 v = -1.959591794 + -2.8 Combine like terms: -1.959591794 + -2.8 = -4.759591794 v = -4.759591794 Simplifying v = -4.759591794Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.840408206, -4.759591794}
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