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Simplifying 2v2 + 8v + 1 = v2 + 9 Reorder the terms: 1 + 8v + 2v2 = v2 + 9 Reorder the terms: 1 + 8v + 2v2 = 9 + v2 Solving 1 + 8v + 2v2 = 9 + v2 Solving for variable 'v'. Reorder the terms: 1 + -9 + 8v + 2v2 + -1v2 = 9 + v2 + -9 + -1v2 Combine like terms: 1 + -9 = -8 -8 + 8v + 2v2 + -1v2 = 9 + v2 + -9 + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -8 + 8v + 1v2 = 9 + v2 + -9 + -1v2 Reorder the terms: -8 + 8v + 1v2 = 9 + -9 + v2 + -1v2 Combine like terms: 9 + -9 = 0 -8 + 8v + 1v2 = 0 + v2 + -1v2 -8 + 8v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -8 + 8v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 8v + 8 + v2 = 0 + 8 Reorder the terms: -8 + 8 + 8v + v2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8v + v2 = 0 + 8 8v + v2 = 0 + 8 Combine like terms: 0 + 8 = 8 8v + v2 = 8 The v term is 8v. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8v + 16 + v2 = 8 + 16 Reorder the terms: 16 + 8v + v2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + 8v + v2 = 24 Factor a perfect square on the left side: (v + 4)(v + 4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (v + 4) equal to 4.898979486 and -4.898979486.Subproblem 1
v + 4 = 4.898979486 Simplifying v + 4 = 4.898979486 Reorder the terms: 4 + v = 4.898979486 Solving 4 + v = 4.898979486 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + v = 4.898979486 + -4 v = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 v = 0.898979486 Simplifying v = 0.898979486Subproblem 2
v + 4 = -4.898979486 Simplifying v + 4 = -4.898979486 Reorder the terms: 4 + v = -4.898979486 Solving 4 + v = -4.898979486 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + v = -4.898979486 + -4 v = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 v = -8.898979486 Simplifying v = -8.898979486Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.898979486, -8.898979486}
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