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Simplifying 4v2 + -25v + 35 = 3 Reorder the terms: 35 + -25v + 4v2 = 3 Solving 35 + -25v + 4v2 = 3 Solving for variable 'v'. Reorder the terms: 35 + -3 + -25v + 4v2 = 3 + -3 Combine like terms: 35 + -3 = 32 32 + -25v + 4v2 = 3 + -3 Combine like terms: 3 + -3 = 0 32 + -25v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8 + -6.25v + v2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6.25v + -8 + v2 = 0 + -8 Reorder the terms: 8 + -8 + -6.25v + v2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6.25v + v2 = 0 + -8 -6.25v + v2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6.25v + v2 = -8 The v term is -6.25v. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25v + 9.765625 + v2 = -8 + 9.765625 Reorder the terms: 9.765625 + -6.25v + v2 = -8 + 9.765625 Combine like terms: -8 + 9.765625 = 1.765625 9.765625 + -6.25v + v2 = 1.765625 Factor a perfect square on the left side: (v + -3.125)(v + -3.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (v + -3.125) equal to 1.328768227 and -1.328768227.Subproblem 1
v + -3.125 = 1.328768227 Simplifying v + -3.125 = 1.328768227 Reorder the terms: -3.125 + v = 1.328768227 Solving -3.125 + v = 1.328768227 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + v = 1.328768227 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + v = 1.328768227 + 3.125 v = 1.328768227 + 3.125 Combine like terms: 1.328768227 + 3.125 = 4.453768227 v = 4.453768227 Simplifying v = 4.453768227Subproblem 2
v + -3.125 = -1.328768227 Simplifying v + -3.125 = -1.328768227 Reorder the terms: -3.125 + v = -1.328768227 Solving -3.125 + v = -1.328768227 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + v = -1.328768227 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + v = -1.328768227 + 3.125 v = -1.328768227 + 3.125 Combine like terms: -1.328768227 + 3.125 = 1.796231773 v = 1.796231773 Simplifying v = 1.796231773Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.453768227, 1.796231773}
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