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Simplifying v2 + -11v + 25 = 0 Reorder the terms: 25 + -11v + v2 = 0 Solving 25 + -11v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -11v + -25 + v2 = 0 + -25 Reorder the terms: 25 + -25 + -11v + v2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -11v + v2 = 0 + -25 -11v + v2 = 0 + -25 Combine like terms: 0 + -25 = -25 -11v + v2 = -25 The v term is -11v. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11v + 30.25 + v2 = -25 + 30.25 Reorder the terms: 30.25 + -11v + v2 = -25 + 30.25 Combine like terms: -25 + 30.25 = 5.25 30.25 + -11v + v2 = 5.25 Factor a perfect square on the left side: (v + -5.5)(v + -5.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (v + -5.5) equal to 2.291287847 and -2.291287847.Subproblem 1
v + -5.5 = 2.291287847 Simplifying v + -5.5 = 2.291287847 Reorder the terms: -5.5 + v = 2.291287847 Solving -5.5 + v = 2.291287847 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = 2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = 2.291287847 + 5.5 v = 2.291287847 + 5.5 Combine like terms: 2.291287847 + 5.5 = 7.791287847 v = 7.791287847 Simplifying v = 7.791287847Subproblem 2
v + -5.5 = -2.291287847 Simplifying v + -5.5 = -2.291287847 Reorder the terms: -5.5 + v = -2.291287847 Solving -5.5 + v = -2.291287847 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = -2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = -2.291287847 + 5.5 v = -2.291287847 + 5.5 Combine like terms: -2.291287847 + 5.5 = 3.208712153 v = 3.208712153 Simplifying v = 3.208712153Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.791287847, 3.208712153}
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