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Simplifying (-3v2 + 6v + -7) + (5v2 + 4v + 1) = 0 Reorder the terms: (-7 + 6v + -3v2) + (5v2 + 4v + 1) = 0 Remove parenthesis around (-7 + 6v + -3v2) -7 + 6v + -3v2 + (5v2 + 4v + 1) = 0 Reorder the terms: -7 + 6v + -3v2 + (1 + 4v + 5v2) = 0 Remove parenthesis around (1 + 4v + 5v2) -7 + 6v + -3v2 + 1 + 4v + 5v2 = 0 Reorder the terms: -7 + 1 + 6v + 4v + -3v2 + 5v2 = 0 Combine like terms: -7 + 1 = -6 -6 + 6v + 4v + -3v2 + 5v2 = 0 Combine like terms: 6v + 4v = 10v -6 + 10v + -3v2 + 5v2 = 0 Combine like terms: -3v2 + 5v2 = 2v2 -6 + 10v + 2v2 = 0 Solving -6 + 10v + 2v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 5v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 5v + v2)' equal to zero and attempt to solve: Simplifying -3 + 5v + v2 = 0 Solving -3 + 5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 5v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + 5v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5v + v2 = 0 + 3 5v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 5v + v2 = 3 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 = 3 + 6.25 Reorder the terms: 6.25 + 5v + v2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + 5v + v2 = 9.25 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (v + 2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
v + 2.5 = 3.041381265 Simplifying v + 2.5 = 3.041381265 Reorder the terms: 2.5 + v = 3.041381265 Solving 2.5 + v = 3.041381265 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 = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = 3.041381265 + -2.5 v = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 v = 0.541381265 Simplifying v = 0.541381265Subproblem 2
v + 2.5 = -3.041381265 Simplifying v + 2.5 = -3.041381265 Reorder the terms: 2.5 + v = -3.041381265 Solving 2.5 + v = -3.041381265 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 = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = -3.041381265 + -2.5 v = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 v = -5.541381265 Simplifying v = -5.541381265Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.541381265, -5.541381265}Solution
v = {0.541381265, -5.541381265}
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