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Simplifying (-7v2 + 4v + -2) + (5v2 + 6v + 1) = 0 Reorder the terms: (-2 + 4v + -7v2) + (5v2 + 6v + 1) = 0 Remove parenthesis around (-2 + 4v + -7v2) -2 + 4v + -7v2 + (5v2 + 6v + 1) = 0 Reorder the terms: -2 + 4v + -7v2 + (1 + 6v + 5v2) = 0 Remove parenthesis around (1 + 6v + 5v2) -2 + 4v + -7v2 + 1 + 6v + 5v2 = 0 Reorder the terms: -2 + 1 + 4v + 6v + -7v2 + 5v2 = 0 Combine like terms: -2 + 1 = -1 -1 + 4v + 6v + -7v2 + 5v2 = 0 Combine like terms: 4v + 6v = 10v -1 + 10v + -7v2 + 5v2 = 0 Combine like terms: -7v2 + 5v2 = -2v2 -1 + 10v + -2v2 = 0 Solving -1 + 10v + -2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -5v + v2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -5v + -0.5 + v2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -5v + v2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -5v + v2 = 0 + -0.5 -5v + v2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -5v + v2 = -0.5 The v term is -5v. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5v + 6.25 + v2 = -0.5 + 6.25 Reorder the terms: 6.25 + -5v + v2 = -0.5 + 6.25 Combine like terms: -0.5 + 6.25 = 5.75 6.25 + -5v + v2 = 5.75 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (v + -2.5) equal to 2.397915762 and -2.397915762.Subproblem 1
v + -2.5 = 2.397915762 Simplifying v + -2.5 = 2.397915762 Reorder the terms: -2.5 + v = 2.397915762 Solving -2.5 + v = 2.397915762 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = 2.397915762 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 2.397915762 + 2.5 v = 2.397915762 + 2.5 Combine like terms: 2.397915762 + 2.5 = 4.897915762 v = 4.897915762 Simplifying v = 4.897915762Subproblem 2
v + -2.5 = -2.397915762 Simplifying v + -2.5 = -2.397915762 Reorder the terms: -2.5 + v = -2.397915762 Solving -2.5 + v = -2.397915762 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = -2.397915762 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = -2.397915762 + 2.5 v = -2.397915762 + 2.5 Combine like terms: -2.397915762 + 2.5 = 0.102084238 v = 0.102084238 Simplifying v = 0.102084238Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.897915762, 0.102084238}
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