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Simplifying -5v2 + 5v + 11 = 0 Reorder the terms: 11 + 5v + -5v2 = 0 Solving 11 + 5v + -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'. -2.2 + -1v + v2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -1v + 2.2 + v2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -1v + v2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -1v + v2 = 0 + 2.2 -1v + v2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -1v + v2 = 2.2 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 2.2 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 2.2 + 0.25 Combine like terms: 2.2 + 0.25 = 2.45 0.25 + -1v + v2 = 2.45 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 2.45 Calculate the square root of the right side: 1.565247584 Break this problem into two subproblems by setting (v + -0.5) equal to 1.565247584 and -1.565247584.Subproblem 1
v + -0.5 = 1.565247584 Simplifying v + -0.5 = 1.565247584 Reorder the terms: -0.5 + v = 1.565247584 Solving -0.5 + v = 1.565247584 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 1.565247584 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 1.565247584 + 0.5 v = 1.565247584 + 0.5 Combine like terms: 1.565247584 + 0.5 = 2.065247584 v = 2.065247584 Simplifying v = 2.065247584Subproblem 2
v + -0.5 = -1.565247584 Simplifying v + -0.5 = -1.565247584 Reorder the terms: -0.5 + v = -1.565247584 Solving -0.5 + v = -1.565247584 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -1.565247584 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -1.565247584 + 0.5 v = -1.565247584 + 0.5 Combine like terms: -1.565247584 + 0.5 = -1.065247584 v = -1.065247584 Simplifying v = -1.065247584Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.065247584, -1.065247584}
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