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Simplifying 4v2 = 18 + -5v Solving 4v2 = 18 + -5v Solving for variable 'v'. Reorder the terms: -18 + 5v + 4v2 = 18 + -5v + -18 + 5v Reorder the terms: -18 + 5v + 4v2 = 18 + -18 + -5v + 5v Combine like terms: 18 + -18 = 0 -18 + 5v + 4v2 = 0 + -5v + 5v -18 + 5v + 4v2 = -5v + 5v Combine like terms: -5v + 5v = 0 -18 + 5v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 1.25v + v2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.25v + 4.5 + v2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.25v + v2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.25v + v2 = 0 + 4.5 1.25v + v2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.25v + v2 = 4.5 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 = 4.5 + 0.390625 Reorder the terms: 0.390625 + 1.25v + v2 = 4.5 + 0.390625 Combine like terms: 4.5 + 0.390625 = 4.890625 0.390625 + 1.25v + v2 = 4.890625 Factor a perfect square on the left side: (v + 0.625)(v + 0.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (v + 0.625) equal to 2.211475752 and -2.211475752.Subproblem 1
v + 0.625 = 2.211475752 Simplifying v + 0.625 = 2.211475752 Reorder the terms: 0.625 + v = 2.211475752 Solving 0.625 + v = 2.211475752 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 = 2.211475752 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + v = 2.211475752 + -0.625 v = 2.211475752 + -0.625 Combine like terms: 2.211475752 + -0.625 = 1.586475752 v = 1.586475752 Simplifying v = 1.586475752Subproblem 2
v + 0.625 = -2.211475752 Simplifying v + 0.625 = -2.211475752 Reorder the terms: 0.625 + v = -2.211475752 Solving 0.625 + v = -2.211475752 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 = -2.211475752 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + v = -2.211475752 + -0.625 v = -2.211475752 + -0.625 Combine like terms: -2.211475752 + -0.625 = -2.836475752 v = -2.836475752 Simplifying v = -2.836475752Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.586475752, -2.836475752}
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