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Simplifying 5v2 + -35v + -28 = 0 Reorder the terms: -28 + -35v + 5v2 = 0 Solving -28 + -35v + 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'. -5.6 + -7v + v2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -7v + 5.6 + v2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -7v + v2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -7v + v2 = 0 + 5.6 -7v + v2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -7v + v2 = 5.6 The v term is -7v. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7v + 12.25 + v2 = 5.6 + 12.25 Reorder the terms: 12.25 + -7v + v2 = 5.6 + 12.25 Combine like terms: 5.6 + 12.25 = 17.85 12.25 + -7v + v2 = 17.85 Factor a perfect square on the left side: (v + -3.5)(v + -3.5) = 17.85 Calculate the square root of the right side: 4.224926035 Break this problem into two subproblems by setting (v + -3.5) equal to 4.224926035 and -4.224926035.Subproblem 1
v + -3.5 = 4.224926035 Simplifying v + -3.5 = 4.224926035 Reorder the terms: -3.5 + v = 4.224926035 Solving -3.5 + v = 4.224926035 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 4.224926035 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 4.224926035 + 3.5 v = 4.224926035 + 3.5 Combine like terms: 4.224926035 + 3.5 = 7.724926035 v = 7.724926035 Simplifying v = 7.724926035Subproblem 2
v + -3.5 = -4.224926035 Simplifying v + -3.5 = -4.224926035 Reorder the terms: -3.5 + v = -4.224926035 Solving -3.5 + v = -4.224926035 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -4.224926035 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -4.224926035 + 3.5 v = -4.224926035 + 3.5 Combine like terms: -4.224926035 + 3.5 = -0.724926035 v = -0.724926035 Simplifying v = -0.724926035Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.724926035, -0.724926035}
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