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Simplifying 2v2 + 7v + -3 = v2 + 25 Reorder the terms: -3 + 7v + 2v2 = v2 + 25 Reorder the terms: -3 + 7v + 2v2 = 25 + v2 Solving -3 + 7v + 2v2 = 25 + v2 Solving for variable 'v'. Reorder the terms: -3 + -25 + 7v + 2v2 + -1v2 = 25 + v2 + -25 + -1v2 Combine like terms: -3 + -25 = -28 -28 + 7v + 2v2 + -1v2 = 25 + v2 + -25 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -28 + 7v + 1v2 = 25 + v2 + -25 + -1v2 Reorder the terms: -28 + 7v + 1v2 = 25 + -25 + v2 + -1v2 Combine like terms: 25 + -25 = 0 -28 + 7v + 1v2 = 0 + v2 + -1v2 -28 + 7v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -28 + 7v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 7v + 28 + v2 = 0 + 28 Reorder the terms: -28 + 28 + 7v + v2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 7v + v2 = 0 + 28 7v + v2 = 0 + 28 Combine like terms: 0 + 28 = 28 7v + v2 = 28 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 = 28 + 12.25 Reorder the terms: 12.25 + 7v + v2 = 28 + 12.25 Combine like terms: 28 + 12.25 = 40.25 12.25 + 7v + v2 = 40.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (v + 3.5) equal to 6.34428877 and -6.34428877.Subproblem 1
v + 3.5 = 6.34428877 Simplifying v + 3.5 = 6.34428877 Reorder the terms: 3.5 + v = 6.34428877 Solving 3.5 + v = 6.34428877 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 = 6.34428877 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 6.34428877 + -3.5 v = 6.34428877 + -3.5 Combine like terms: 6.34428877 + -3.5 = 2.84428877 v = 2.84428877 Simplifying v = 2.84428877Subproblem 2
v + 3.5 = -6.34428877 Simplifying v + 3.5 = -6.34428877 Reorder the terms: 3.5 + v = -6.34428877 Solving 3.5 + v = -6.34428877 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 = -6.34428877 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -6.34428877 + -3.5 v = -6.34428877 + -3.5 Combine like terms: -6.34428877 + -3.5 = -9.84428877 v = -9.84428877 Simplifying v = -9.84428877Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.84428877, -9.84428877}
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