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Simplifying 3 + -8v + -5v2 = 2v Solving 3 + -8v + -5v2 = 2v Solving for variable 'v'. Reorder the terms: 3 + -8v + -2v + -5v2 = 2v + -2v Combine like terms: -8v + -2v = -10v 3 + -10v + -5v2 = 2v + -2v Combine like terms: 2v + -2v = 0 3 + -10v + -5v2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + 2v + v2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 2v + 0.6 + v2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 2v + v2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 2v + v2 = 0 + 0.6 2v + v2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 2v + v2 = 0.6 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 0.6 + 1 Reorder the terms: 1 + 2v + v2 = 0.6 + 1 Combine like terms: 0.6 + 1 = 1.6 1 + 2v + v2 = 1.6 Factor a perfect square on the left side: (v + 1)(v + 1) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (v + 1) equal to 1.264911064 and -1.264911064.Subproblem 1
v + 1 = 1.264911064 Simplifying v + 1 = 1.264911064 Reorder the terms: 1 + v = 1.264911064 Solving 1 + v = 1.264911064 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 1.264911064 + -1 Combine like terms: 1 + -1 = 0 0 + v = 1.264911064 + -1 v = 1.264911064 + -1 Combine like terms: 1.264911064 + -1 = 0.264911064 v = 0.264911064 Simplifying v = 0.264911064Subproblem 2
v + 1 = -1.264911064 Simplifying v + 1 = -1.264911064 Reorder the terms: 1 + v = -1.264911064 Solving 1 + v = -1.264911064 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -1.264911064 + -1 Combine like terms: 1 + -1 = 0 0 + v = -1.264911064 + -1 v = -1.264911064 + -1 Combine like terms: -1.264911064 + -1 = -2.264911064 v = -2.264911064 Simplifying v = -2.264911064Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.264911064, -2.264911064}
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