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Simplifying 4v2 + -10 = 9v Reorder the terms: -10 + 4v2 = 9v Solving -10 + 4v2 = 9v Solving for variable 'v'. Reorder the terms: -10 + -9v + 4v2 = 9v + -9v Combine like terms: 9v + -9v = 0 -10 + -9v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + -2.25v + v2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.25v + 2.5 + v2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.25v + v2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.25v + v2 = 0 + 2.5 -2.25v + v2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.25v + v2 = 2.5 The v term is -2.25v. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25v + 1.265625 + v2 = 2.5 + 1.265625 Reorder the terms: 1.265625 + -2.25v + v2 = 2.5 + 1.265625 Combine like terms: 2.5 + 1.265625 = 3.765625 1.265625 + -2.25v + v2 = 3.765625 Factor a perfect square on the left side: (v + -1.125)(v + -1.125) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (v + -1.125) equal to 1.940521837 and -1.940521837.Subproblem 1
v + -1.125 = 1.940521837 Simplifying v + -1.125 = 1.940521837 Reorder the terms: -1.125 + v = 1.940521837 Solving -1.125 + v = 1.940521837 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + v = 1.940521837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + v = 1.940521837 + 1.125 v = 1.940521837 + 1.125 Combine like terms: 1.940521837 + 1.125 = 3.065521837 v = 3.065521837 Simplifying v = 3.065521837Subproblem 2
v + -1.125 = -1.940521837 Simplifying v + -1.125 = -1.940521837 Reorder the terms: -1.125 + v = -1.940521837 Solving -1.125 + v = -1.940521837 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + v = -1.940521837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + v = -1.940521837 + 1.125 v = -1.940521837 + 1.125 Combine like terms: -1.940521837 + 1.125 = -0.815521837 v = -0.815521837 Simplifying v = -0.815521837Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.065521837, -0.815521837}
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