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Simplifying 18v2 + -7v + -3 = 0 Reorder the terms: -3 + -7v + 18v2 = 0 Solving -3 + -7v + 18v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1666666667 + -0.3888888889v + v2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.3888888889v + 0.1666666667 + v2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.3888888889v + v2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.3888888889v + v2 = 0 + 0.1666666667 -0.3888888889v + v2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.3888888889v + v2 = 0.1666666667 The v term is -0.3888888889v. Take half its coefficient (-0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. -0.3888888889v + 0.03780864200 + v2 = 0.1666666667 + 0.03780864200 Reorder the terms: 0.03780864200 + -0.3888888889v + v2 = 0.1666666667 + 0.03780864200 Combine like terms: 0.1666666667 + 0.03780864200 = 0.2044753087 0.03780864200 + -0.3888888889v + v2 = 0.2044753087 Factor a perfect square on the left side: (v + -0.1944444445)(v + -0.1944444445) = 0.2044753087 Calculate the square root of the right side: 0.452189461 Break this problem into two subproblems by setting (v + -0.1944444445) equal to 0.452189461 and -0.452189461.Subproblem 1
v + -0.1944444445 = 0.452189461 Simplifying v + -0.1944444445 = 0.452189461 Reorder the terms: -0.1944444445 + v = 0.452189461 Solving -0.1944444445 + v = 0.452189461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + v = 0.452189461 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + v = 0.452189461 + 0.1944444445 v = 0.452189461 + 0.1944444445 Combine like terms: 0.452189461 + 0.1944444445 = 0.6466339055 v = 0.6466339055 Simplifying v = 0.6466339055Subproblem 2
v + -0.1944444445 = -0.452189461 Simplifying v + -0.1944444445 = -0.452189461 Reorder the terms: -0.1944444445 + v = -0.452189461 Solving -0.1944444445 + v = -0.452189461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + v = -0.452189461 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + v = -0.452189461 + 0.1944444445 v = -0.452189461 + 0.1944444445 Combine like terms: -0.452189461 + 0.1944444445 = -0.2577450165 v = -0.2577450165 Simplifying v = -0.2577450165Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.6466339055, -0.2577450165}
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