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Simplifying (v + 3)(v + -4) = v Reorder the terms: (3 + v)(v + -4) = v Reorder the terms: (3 + v)(-4 + v) = v Multiply (3 + v) * (-4 + v) (3(-4 + v) + v(-4 + v)) = v ((-4 * 3 + v * 3) + v(-4 + v)) = v ((-12 + 3v) + v(-4 + v)) = v (-12 + 3v + (-4 * v + v * v)) = v (-12 + 3v + (-4v + v2)) = v Combine like terms: 3v + -4v = -1v (-12 + -1v + v2) = v Solving -12 + -1v + v2 = v Solving for variable 'v'. Reorder the terms: -12 + -1v + -1v + v2 = v + -1v Combine like terms: -1v + -1v = -2v -12 + -2v + v2 = v + -1v Combine like terms: v + -1v = 0 -12 + -2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -2v + 12 + v2 = 0 + 12 Reorder the terms: -12 + 12 + -2v + v2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2v + v2 = 0 + 12 -2v + v2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2v + v2 = 12 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 = 12 + 1 Reorder the terms: 1 + -2v + v2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + -2v + v2 = 13 Factor a perfect square on the left side: (v + -1)(v + -1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (v + -1) equal to 3.605551275 and -3.605551275.Subproblem 1
v + -1 = 3.605551275 Simplifying v + -1 = 3.605551275 Reorder the terms: -1 + v = 3.605551275 Solving -1 + v = 3.605551275 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 = 3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + v = 3.605551275 + 1 v = 3.605551275 + 1 Combine like terms: 3.605551275 + 1 = 4.605551275 v = 4.605551275 Simplifying v = 4.605551275Subproblem 2
v + -1 = -3.605551275 Simplifying v + -1 = -3.605551275 Reorder the terms: -1 + v = -3.605551275 Solving -1 + v = -3.605551275 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 = -3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + v = -3.605551275 + 1 v = -3.605551275 + 1 Combine like terms: -3.605551275 + 1 = -2.605551275 v = -2.605551275 Simplifying v = -2.605551275Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.605551275, -2.605551275}
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