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Simplifying 4v2 + -10v + 3 = 0 Reorder the terms: 3 + -10v + 4v2 = 0 Solving 3 + -10v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -2.5v + v2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.5v + -0.75 + v2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.5v + v2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.5v + v2 = 0 + -0.75 -2.5v + v2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.5v + v2 = -0.75 The v term is -2.5v. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5v + 1.5625 + v2 = -0.75 + 1.5625 Reorder the terms: 1.5625 + -2.5v + v2 = -0.75 + 1.5625 Combine like terms: -0.75 + 1.5625 = 0.8125 1.5625 + -2.5v + v2 = 0.8125 Factor a perfect square on the left side: (v + -1.25)(v + -1.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (v + -1.25) equal to 0.901387819 and -0.901387819.Subproblem 1
v + -1.25 = 0.901387819 Simplifying v + -1.25 = 0.901387819 Reorder the terms: -1.25 + v = 0.901387819 Solving -1.25 + v = 0.901387819 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + v = 0.901387819 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + v = 0.901387819 + 1.25 v = 0.901387819 + 1.25 Combine like terms: 0.901387819 + 1.25 = 2.151387819 v = 2.151387819 Simplifying v = 2.151387819Subproblem 2
v + -1.25 = -0.901387819 Simplifying v + -1.25 = -0.901387819 Reorder the terms: -1.25 + v = -0.901387819 Solving -1.25 + v = -0.901387819 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + v = -0.901387819 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + v = -0.901387819 + 1.25 v = -0.901387819 + 1.25 Combine like terms: -0.901387819 + 1.25 = 0.348612181 v = 0.348612181 Simplifying v = 0.348612181Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.151387819, 0.348612181}
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