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Simplifying 4v2 + -32 = -18 + -5v Reorder the terms: -32 + 4v2 = -18 + -5v Solving -32 + 4v2 = -18 + -5v Solving for variable 'v'. Reorder the terms: -32 + 18 + 5v + 4v2 = -18 + -5v + 18 + 5v Combine like terms: -32 + 18 = -14 -14 + 5v + 4v2 = -18 + -5v + 18 + 5v Reorder the terms: -14 + 5v + 4v2 = -18 + 18 + -5v + 5v Combine like terms: -18 + 18 = 0 -14 + 5v + 4v2 = 0 + -5v + 5v -14 + 5v + 4v2 = -5v + 5v Combine like terms: -5v + 5v = 0 -14 + 5v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + 1.25v + v2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 1.25v + 3.5 + v2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 1.25v + v2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 1.25v + v2 = 0 + 3.5 1.25v + v2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 1.25v + v2 = 3.5 The v term is 1.25v. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25v + 0.390625 + v2 = 3.5 + 0.390625 Reorder the terms: 0.390625 + 1.25v + v2 = 3.5 + 0.390625 Combine like terms: 3.5 + 0.390625 = 3.890625 0.390625 + 1.25v + v2 = 3.890625 Factor a perfect square on the left side: (v + 0.625)(v + 0.625) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (v + 0.625) equal to 1.97246673 and -1.97246673.Subproblem 1
v + 0.625 = 1.97246673 Simplifying v + 0.625 = 1.97246673 Reorder the terms: 0.625 + v = 1.97246673 Solving 0.625 + v = 1.97246673 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + v = 1.97246673 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + v = 1.97246673 + -0.625 v = 1.97246673 + -0.625 Combine like terms: 1.97246673 + -0.625 = 1.34746673 v = 1.34746673 Simplifying v = 1.34746673Subproblem 2
v + 0.625 = -1.97246673 Simplifying v + 0.625 = -1.97246673 Reorder the terms: 0.625 + v = -1.97246673 Solving 0.625 + v = -1.97246673 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + v = -1.97246673 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + v = -1.97246673 + -0.625 v = -1.97246673 + -0.625 Combine like terms: -1.97246673 + -0.625 = -2.59746673 v = -2.59746673 Simplifying v = -2.59746673Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.34746673, -2.59746673}
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