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Simplifying 6v2 + -7v = 17 Reorder the terms: -7v + 6v2 = 17 Solving -7v + 6v2 = 17 Solving for variable 'v'. Reorder the terms: -17 + -7v + 6v2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -7v + 6v2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + -1.166666667v + v2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + -1.166666667v + 2.833333333 + v2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + -1.166666667v + v2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + -1.166666667v + v2 = 0 + 2.833333333 -1.166666667v + v2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 -1.166666667v + v2 = 2.833333333 The v term is -1.166666667v. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667v + 0.3402777780 + v2 = 2.833333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667v + v2 = 2.833333333 + 0.3402777780 Combine like terms: 2.833333333 + 0.3402777780 = 3.173611111 0.3402777780 + -1.166666667v + v2 = 3.173611111 Factor a perfect square on the left side: (v + -0.5833333335)(v + -0.5833333335) = 3.173611111 Calculate the square root of the right side: 1.781463194 Break this problem into two subproblems by setting (v + -0.5833333335) equal to 1.781463194 and -1.781463194.Subproblem 1
v + -0.5833333335 = 1.781463194 Simplifying v + -0.5833333335 = 1.781463194 Reorder the terms: -0.5833333335 + v = 1.781463194 Solving -0.5833333335 + v = 1.781463194 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + v = 1.781463194 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + v = 1.781463194 + 0.5833333335 v = 1.781463194 + 0.5833333335 Combine like terms: 1.781463194 + 0.5833333335 = 2.3647965275 v = 2.3647965275 Simplifying v = 2.3647965275Subproblem 2
v + -0.5833333335 = -1.781463194 Simplifying v + -0.5833333335 = -1.781463194 Reorder the terms: -0.5833333335 + v = -1.781463194 Solving -0.5833333335 + v = -1.781463194 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + v = -1.781463194 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + v = -1.781463194 + 0.5833333335 v = -1.781463194 + 0.5833333335 Combine like terms: -1.781463194 + 0.5833333335 = -1.1981298605 v = -1.1981298605 Simplifying v = -1.1981298605Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.3647965275, -1.1981298605}
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