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Simplifying 5v2 + 8v + -16 = 0 Reorder the terms: -16 + 8v + 5v2 = 0 Solving -16 + 8v + 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'. -3.2 + 1.6v + v2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 1.6v + 3.2 + v2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 1.6v + v2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 1.6v + v2 = 0 + 3.2 1.6v + v2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 1.6v + v2 = 3.2 The v term is 1.6v. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6v + 0.64 + v2 = 3.2 + 0.64 Reorder the terms: 0.64 + 1.6v + v2 = 3.2 + 0.64 Combine like terms: 3.2 + 0.64 = 3.84 0.64 + 1.6v + v2 = 3.84 Factor a perfect square on the left side: (v + 0.8)(v + 0.8) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (v + 0.8) equal to 1.959591794 and -1.959591794.Subproblem 1
v + 0.8 = 1.959591794 Simplifying v + 0.8 = 1.959591794 Reorder the terms: 0.8 + v = 1.959591794 Solving 0.8 + v = 1.959591794 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + v = 1.959591794 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = 1.959591794 + -0.8 v = 1.959591794 + -0.8 Combine like terms: 1.959591794 + -0.8 = 1.159591794 v = 1.159591794 Simplifying v = 1.159591794Subproblem 2
v + 0.8 = -1.959591794 Simplifying v + 0.8 = -1.959591794 Reorder the terms: 0.8 + v = -1.959591794 Solving 0.8 + v = -1.959591794 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + v = -1.959591794 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + v = -1.959591794 + -0.8 v = -1.959591794 + -0.8 Combine like terms: -1.959591794 + -0.8 = -2.759591794 v = -2.759591794 Simplifying v = -2.759591794Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.159591794, -2.759591794}
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