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Simplifying v2 + 5v = 8 Reorder the terms: 5v + v2 = 8 Solving 5v + v2 = 8 Solving for variable 'v'. Reorder the terms: -8 + 5v + v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 5v + 8 + v2 = 0 + 8 Reorder the terms: -8 + 8 + 5v + v2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5v + v2 = 0 + 8 5v + v2 = 0 + 8 Combine like terms: 0 + 8 = 8 5v + v2 = 8 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 = 8 + 6.25 Reorder the terms: 6.25 + 5v + v2 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + 5v + v2 = 14.25 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (v + 2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
v + 2.5 = 3.774917218 Simplifying v + 2.5 = 3.774917218 Reorder the terms: 2.5 + v = 3.774917218 Solving 2.5 + v = 3.774917218 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 = 3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = 3.774917218 + -2.5 v = 3.774917218 + -2.5 Combine like terms: 3.774917218 + -2.5 = 1.274917218 v = 1.274917218 Simplifying v = 1.274917218Subproblem 2
v + 2.5 = -3.774917218 Simplifying v + 2.5 = -3.774917218 Reorder the terms: 2.5 + v = -3.774917218 Solving 2.5 + v = -3.774917218 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 = -3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = -3.774917218 + -2.5 v = -3.774917218 + -2.5 Combine like terms: -3.774917218 + -2.5 = -6.274917218 v = -6.274917218 Simplifying v = -6.274917218Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.274917218, -6.274917218}
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