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Simplifying v2 + -1v + -10 = 0 Reorder the terms: -10 + -1v + v2 = 0 Solving -10 + -1v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -1v + 10 + v2 = 0 + 10 Reorder the terms: -10 + 10 + -1v + v2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1v + v2 = 0 + 10 -1v + v2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1v + v2 = 10 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 10 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + -1v + v2 = 10.25 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (v + -0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
v + -0.5 = 3.201562119 Simplifying v + -0.5 = 3.201562119 Reorder the terms: -0.5 + v = 3.201562119 Solving -0.5 + v = 3.201562119 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 3.201562119 + 0.5 v = 3.201562119 + 0.5 Combine like terms: 3.201562119 + 0.5 = 3.701562119 v = 3.701562119 Simplifying v = 3.701562119Subproblem 2
v + -0.5 = -3.201562119 Simplifying v + -0.5 = -3.201562119 Reorder the terms: -0.5 + v = -3.201562119 Solving -0.5 + v = -3.201562119 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -3.201562119 + 0.5 v = -3.201562119 + 0.5 Combine like terms: -3.201562119 + 0.5 = -2.701562119 v = -2.701562119 Simplifying v = -2.701562119Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.701562119, -2.701562119}
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