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Simplifying 2v2 + 8v + -16 = 10 Reorder the terms: -16 + 8v + 2v2 = 10 Solving -16 + 8v + 2v2 = 10 Solving for variable 'v'. Reorder the terms: -16 + -10 + 8v + 2v2 = 10 + -10 Combine like terms: -16 + -10 = -26 -26 + 8v + 2v2 = 10 + -10 Combine like terms: 10 + -10 = 0 -26 + 8v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 4v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 4v + v2)' equal to zero and attempt to solve: Simplifying -13 + 4v + v2 = 0 Solving -13 + 4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 4v + 13 + v2 = 0 + 13 Reorder the terms: -13 + 13 + 4v + v2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4v + v2 = 0 + 13 4v + v2 = 0 + 13 Combine like terms: 0 + 13 = 13 4v + v2 = 13 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 13 + 4 Reorder the terms: 4 + 4v + v2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + 4v + v2 = 17 Factor a perfect square on the left side: (v + 2)(v + 2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (v + 2) equal to 4.123105626 and -4.123105626.Subproblem 1
v + 2 = 4.123105626 Simplifying v + 2 = 4.123105626 Reorder the terms: 2 + v = 4.123105626 Solving 2 + v = 4.123105626 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + v = 4.123105626 + -2 v = 4.123105626 + -2 Combine like terms: 4.123105626 + -2 = 2.123105626 v = 2.123105626 Simplifying v = 2.123105626Subproblem 2
v + 2 = -4.123105626 Simplifying v + 2 = -4.123105626 Reorder the terms: 2 + v = -4.123105626 Solving 2 + v = -4.123105626 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + v = -4.123105626 + -2 v = -4.123105626 + -2 Combine like terms: -4.123105626 + -2 = -6.123105626 v = -6.123105626 Simplifying v = -6.123105626Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.123105626, -6.123105626}Solution
v = {2.123105626, -6.123105626}
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