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Simplifying v2 + -19v + 28 = 0 Reorder the terms: 28 + -19v + v2 = 0 Solving 28 + -19v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -19v + -28 + v2 = 0 + -28 Reorder the terms: 28 + -28 + -19v + v2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -19v + v2 = 0 + -28 -19v + v2 = 0 + -28 Combine like terms: 0 + -28 = -28 -19v + v2 = -28 The v term is -19v. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19v + 90.25 + v2 = -28 + 90.25 Reorder the terms: 90.25 + -19v + v2 = -28 + 90.25 Combine like terms: -28 + 90.25 = 62.25 90.25 + -19v + v2 = 62.25 Factor a perfect square on the left side: (v + -9.5)(v + -9.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (v + -9.5) equal to 7.889866919 and -7.889866919.Subproblem 1
v + -9.5 = 7.889866919 Simplifying v + -9.5 = 7.889866919 Reorder the terms: -9.5 + v = 7.889866919 Solving -9.5 + v = 7.889866919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + v = 7.889866919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + v = 7.889866919 + 9.5 v = 7.889866919 + 9.5 Combine like terms: 7.889866919 + 9.5 = 17.389866919 v = 17.389866919 Simplifying v = 17.389866919Subproblem 2
v + -9.5 = -7.889866919 Simplifying v + -9.5 = -7.889866919 Reorder the terms: -9.5 + v = -7.889866919 Solving -9.5 + v = -7.889866919 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + v = -7.889866919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + v = -7.889866919 + 9.5 v = -7.889866919 + 9.5 Combine like terms: -7.889866919 + 9.5 = 1.610133081 v = 1.610133081 Simplifying v = 1.610133081Solution
The solution to the problem is based on the solutions from the subproblems. v = {17.389866919, 1.610133081}
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