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Simplifying 4v2 + 16v = 35 Reorder the terms: 16v + 4v2 = 35 Solving 16v + 4v2 = 35 Solving for variable 'v'. Reorder the terms: -35 + 16v + 4v2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 16v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 4v + v2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 4v + 8.75 + v2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 4v + v2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 4v + v2 = 0 + 8.75 4v + v2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 4v + v2 = 8.75 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 8.75 + 4 Reorder the terms: 4 + 4v + v2 = 8.75 + 4 Combine like terms: 8.75 + 4 = 12.75 4 + 4v + v2 = 12.75 Factor a perfect square on the left side: (v + 2)(v + 2) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (v + 2) equal to 3.570714214 and -3.570714214.Subproblem 1
v + 2 = 3.570714214 Simplifying v + 2 = 3.570714214 Reorder the terms: 2 + v = 3.570714214 Solving 2 + v = 3.570714214 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 3.570714214 + -2 Combine like terms: 2 + -2 = 0 0 + v = 3.570714214 + -2 v = 3.570714214 + -2 Combine like terms: 3.570714214 + -2 = 1.570714214 v = 1.570714214 Simplifying v = 1.570714214Subproblem 2
v + 2 = -3.570714214 Simplifying v + 2 = -3.570714214 Reorder the terms: 2 + v = -3.570714214 Solving 2 + v = -3.570714214 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -3.570714214 + -2 Combine like terms: 2 + -2 = 0 0 + v = -3.570714214 + -2 v = -3.570714214 + -2 Combine like terms: -3.570714214 + -2 = -5.570714214 v = -5.570714214 Simplifying v = -5.570714214Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.570714214, -5.570714214}
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