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Simplifying v2 + 6.1v + -6 = 0 Reorder the terms: -6 + 6.1v + v2 = 0 Solving -6 + 6.1v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 6.1v + 6 + v2 = 0 + 6 Reorder the terms: -6 + 6 + 6.1v + v2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6.1v + v2 = 0 + 6 6.1v + v2 = 0 + 6 Combine like terms: 0 + 6 = 6 6.1v + v2 = 6 The v term is 6.1v. Take half its coefficient (3.05). Square it (9.3025) and add it to both sides. Add '9.3025' to each side of the equation. 6.1v + 9.3025 + v2 = 6 + 9.3025 Reorder the terms: 9.3025 + 6.1v + v2 = 6 + 9.3025 Combine like terms: 6 + 9.3025 = 15.3025 9.3025 + 6.1v + v2 = 15.3025 Factor a perfect square on the left side: (v + 3.05)(v + 3.05) = 15.3025 Calculate the square root of the right side: 3.911840999 Break this problem into two subproblems by setting (v + 3.05) equal to 3.911840999 and -3.911840999.Subproblem 1
v + 3.05 = 3.911840999 Simplifying v + 3.05 = 3.911840999 Reorder the terms: 3.05 + v = 3.911840999 Solving 3.05 + v = 3.911840999 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.05' to each side of the equation. 3.05 + -3.05 + v = 3.911840999 + -3.05 Combine like terms: 3.05 + -3.05 = 0.00 0.00 + v = 3.911840999 + -3.05 v = 3.911840999 + -3.05 Combine like terms: 3.911840999 + -3.05 = 0.861840999 v = 0.861840999 Simplifying v = 0.861840999Subproblem 2
v + 3.05 = -3.911840999 Simplifying v + 3.05 = -3.911840999 Reorder the terms: 3.05 + v = -3.911840999 Solving 3.05 + v = -3.911840999 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.05' to each side of the equation. 3.05 + -3.05 + v = -3.911840999 + -3.05 Combine like terms: 3.05 + -3.05 = 0.00 0.00 + v = -3.911840999 + -3.05 v = -3.911840999 + -3.05 Combine like terms: -3.911840999 + -3.05 = -6.961840999 v = -6.961840999 Simplifying v = -6.961840999Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.861840999, -6.961840999}
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