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Simplifying 5v2 + -10v + -10 = 0 Reorder the terms: -10 + -10v + 5v2 = 0 Solving -10 + -10v + 5v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + -2v + v2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -2v + v2)' equal to zero and attempt to solve: Simplifying -2 + -2v + v2 = 0 Solving -2 + -2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + -2v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2v + v2 = 0 + 2 -2v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2v + v2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2v + v2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2v + v2 = 3 Factor a perfect square on the left side: (v + -1)(v + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (v + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
v + -1 = 1.732050808 Simplifying v + -1 = 1.732050808 Reorder the terms: -1 + v = 1.732050808 Solving -1 + v = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + v = 1.732050808 + 1 v = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 v = 2.732050808 Simplifying v = 2.732050808Subproblem 2
v + -1 = -1.732050808 Simplifying v + -1 = -1.732050808 Reorder the terms: -1 + v = -1.732050808 Solving -1 + v = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + v = -1.732050808 + 1 v = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 v = -0.732050808 Simplifying v = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.732050808, -0.732050808}Solution
v = {2.732050808, -0.732050808}
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