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Simplifying 4v2 + -15v + 2 = 0 Reorder the terms: 2 + -15v + 4v2 = 0 Solving 2 + -15v + 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'. 0.5 + -3.75v + v2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.75v + -0.5 + v2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.75v + v2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.75v + v2 = 0 + -0.5 -3.75v + v2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.75v + v2 = -0.5 The v term is -3.75v. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75v + 3.515625 + v2 = -0.5 + 3.515625 Reorder the terms: 3.515625 + -3.75v + v2 = -0.5 + 3.515625 Combine like terms: -0.5 + 3.515625 = 3.015625 3.515625 + -3.75v + v2 = 3.015625 Factor a perfect square on the left side: (v + -1.875)(v + -1.875) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (v + -1.875) equal to 1.736555499 and -1.736555499.Subproblem 1
v + -1.875 = 1.736555499 Simplifying v + -1.875 = 1.736555499 Reorder the terms: -1.875 + v = 1.736555499 Solving -1.875 + v = 1.736555499 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + v = 1.736555499 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + v = 1.736555499 + 1.875 v = 1.736555499 + 1.875 Combine like terms: 1.736555499 + 1.875 = 3.611555499 v = 3.611555499 Simplifying v = 3.611555499Subproblem 2
v + -1.875 = -1.736555499 Simplifying v + -1.875 = -1.736555499 Reorder the terms: -1.875 + v = -1.736555499 Solving -1.875 + v = -1.736555499 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + v = -1.736555499 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + v = -1.736555499 + 1.875 v = -1.736555499 + 1.875 Combine like terms: -1.736555499 + 1.875 = 0.138444501 v = 0.138444501 Simplifying v = 0.138444501Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.611555499, 0.138444501}
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