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Simplifying 6v2 + 12v + -52 = 2 Reorder the terms: -52 + 12v + 6v2 = 2 Solving -52 + 12v + 6v2 = 2 Solving for variable 'v'. Reorder the terms: -52 + -2 + 12v + 6v2 = 2 + -2 Combine like terms: -52 + -2 = -54 -54 + 12v + 6v2 = 2 + -2 Combine like terms: 2 + -2 = 0 -54 + 12v + 6v2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + 2v + v2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + 2v + v2)' equal to zero and attempt to solve: Simplifying -9 + 2v + v2 = 0 Solving -9 + 2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 2v + 9 + v2 = 0 + 9 Reorder the terms: -9 + 9 + 2v + v2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2v + v2 = 0 + 9 2v + v2 = 0 + 9 Combine like terms: 0 + 9 = 9 2v + v2 = 9 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 = 9 + 1 Reorder the terms: 1 + 2v + v2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2v + v2 = 10 Factor a perfect square on the left side: (v + 1)(v + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (v + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
v + 1 = 3.16227766 Simplifying v + 1 = 3.16227766 Reorder the terms: 1 + v = 3.16227766 Solving 1 + v = 3.16227766 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 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + v = 3.16227766 + -1 v = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 v = 2.16227766 Simplifying v = 2.16227766Subproblem 2
v + 1 = -3.16227766 Simplifying v + 1 = -3.16227766 Reorder the terms: 1 + v = -3.16227766 Solving 1 + v = -3.16227766 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 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + v = -3.16227766 + -1 v = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 v = -4.16227766 Simplifying v = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.16227766, -4.16227766}Solution
v = {2.16227766, -4.16227766}
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