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Simplifying 7v2 + -3v + -27 = 0 Reorder the terms: -27 + -3v + 7v2 = 0 Solving -27 + -3v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.857142857 + -0.4285714286v + v2 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + -0.4285714286v + 3.857142857 + v2 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + -0.4285714286v + v2 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + -0.4285714286v + v2 = 0 + 3.857142857 -0.4285714286v + v2 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 -0.4285714286v + v2 = 3.857142857 The v term is -0.4285714286v. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286v + 0.04591836735 + v2 = 3.857142857 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286v + v2 = 3.857142857 + 0.04591836735 Combine like terms: 3.857142857 + 0.04591836735 = 3.90306122435 0.04591836735 + -0.4285714286v + v2 = 3.90306122435 Factor a perfect square on the left side: (v + -0.2142857143)(v + -0.2142857143) = 3.90306122435 Calculate the square root of the right side: 1.975616669 Break this problem into two subproblems by setting (v + -0.2142857143) equal to 1.975616669 and -1.975616669.Subproblem 1
v + -0.2142857143 = 1.975616669 Simplifying v + -0.2142857143 = 1.975616669 Reorder the terms: -0.2142857143 + v = 1.975616669 Solving -0.2142857143 + v = 1.975616669 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + v = 1.975616669 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + v = 1.975616669 + 0.2142857143 v = 1.975616669 + 0.2142857143 Combine like terms: 1.975616669 + 0.2142857143 = 2.1899023833 v = 2.1899023833 Simplifying v = 2.1899023833Subproblem 2
v + -0.2142857143 = -1.975616669 Simplifying v + -0.2142857143 = -1.975616669 Reorder the terms: -0.2142857143 + v = -1.975616669 Solving -0.2142857143 + v = -1.975616669 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + v = -1.975616669 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + v = -1.975616669 + 0.2142857143 v = -1.975616669 + 0.2142857143 Combine like terms: -1.975616669 + 0.2142857143 = -1.7613309547 v = -1.7613309547 Simplifying v = -1.7613309547Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.1899023833, -1.7613309547}
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