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Simplifying v2 + 13v = 20 Reorder the terms: 13v + v2 = 20 Solving 13v + v2 = 20 Solving for variable 'v'. Reorder the terms: -20 + 13v + v2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 13v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 13v + 20 + v2 = 0 + 20 Reorder the terms: -20 + 20 + 13v + v2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 13v + v2 = 0 + 20 13v + v2 = 0 + 20 Combine like terms: 0 + 20 = 20 13v + v2 = 20 The v term is 13v. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13v + 42.25 + v2 = 20 + 42.25 Reorder the terms: 42.25 + 13v + v2 = 20 + 42.25 Combine like terms: 20 + 42.25 = 62.25 42.25 + 13v + v2 = 62.25 Factor a perfect square on the left side: (v + 6.5)(v + 6.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (v + 6.5) equal to 7.889866919 and -7.889866919.Subproblem 1
v + 6.5 = 7.889866919 Simplifying v + 6.5 = 7.889866919 Reorder the terms: 6.5 + v = 7.889866919 Solving 6.5 + v = 7.889866919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + v = 7.889866919 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + v = 7.889866919 + -6.5 v = 7.889866919 + -6.5 Combine like terms: 7.889866919 + -6.5 = 1.389866919 v = 1.389866919 Simplifying v = 1.389866919Subproblem 2
v + 6.5 = -7.889866919 Simplifying v + 6.5 = -7.889866919 Reorder the terms: 6.5 + v = -7.889866919 Solving 6.5 + v = -7.889866919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + v = -7.889866919 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + v = -7.889866919 + -6.5 v = -7.889866919 + -6.5 Combine like terms: -7.889866919 + -6.5 = -14.389866919 v = -14.389866919 Simplifying v = -14.389866919Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.389866919, -14.389866919}
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