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Simplifying v2 = -3 + -7v Solving v2 = -3 + -7v Solving for variable 'v'. Reorder the terms: 3 + 7v + v2 = -3 + -7v + 3 + 7v Reorder the terms: 3 + 7v + v2 = -3 + 3 + -7v + 7v Combine like terms: -3 + 3 = 0 3 + 7v + v2 = 0 + -7v + 7v 3 + 7v + v2 = -7v + 7v Combine like terms: -7v + 7v = 0 3 + 7v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7v + -3 + v2 = 0 + -3 Reorder the terms: 3 + -3 + 7v + v2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7v + v2 = 0 + -3 7v + v2 = 0 + -3 Combine like terms: 0 + -3 = -3 7v + v2 = -3 The v term is 7v. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7v + 12.25 + v2 = -3 + 12.25 Reorder the terms: 12.25 + 7v + v2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + 7v + v2 = 9.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (v + 3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
v + 3.5 = 3.041381265 Simplifying v + 3.5 = 3.041381265 Reorder the terms: 3.5 + v = 3.041381265 Solving 3.5 + v = 3.041381265 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 3.041381265 + -3.5 v = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 v = -0.458618735 Simplifying v = -0.458618735Subproblem 2
v + 3.5 = -3.041381265 Simplifying v + 3.5 = -3.041381265 Reorder the terms: 3.5 + v = -3.041381265 Solving 3.5 + v = -3.041381265 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -3.041381265 + -3.5 v = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 v = -6.541381265 Simplifying v = -6.541381265Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.458618735, -6.541381265}
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