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Simplifying v2 + -2v + -101 = -8 Reorder the terms: -101 + -2v + v2 = -8 Solving -101 + -2v + v2 = -8 Solving for variable 'v'. Reorder the terms: -101 + 8 + -2v + v2 = -8 + 8 Combine like terms: -101 + 8 = -93 -93 + -2v + v2 = -8 + 8 Combine like terms: -8 + 8 = 0 -93 + -2v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '93' to each side of the equation. -93 + -2v + 93 + v2 = 0 + 93 Reorder the terms: -93 + 93 + -2v + v2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + -2v + v2 = 0 + 93 -2v + v2 = 0 + 93 Combine like terms: 0 + 93 = 93 -2v + v2 = 93 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 93 + 1 Reorder the terms: 1 + -2v + v2 = 93 + 1 Combine like terms: 93 + 1 = 94 1 + -2v + v2 = 94 Factor a perfect square on the left side: (v + -1)(v + -1) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (v + -1) equal to 9.695359715 and -9.695359715.Subproblem 1
v + -1 = 9.695359715 Simplifying v + -1 = 9.695359715 Reorder the terms: -1 + v = 9.695359715 Solving -1 + v = 9.695359715 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 9.695359715 + 1 Combine like terms: -1 + 1 = 0 0 + v = 9.695359715 + 1 v = 9.695359715 + 1 Combine like terms: 9.695359715 + 1 = 10.695359715 v = 10.695359715 Simplifying v = 10.695359715Subproblem 2
v + -1 = -9.695359715 Simplifying v + -1 = -9.695359715 Reorder the terms: -1 + v = -9.695359715 Solving -1 + v = -9.695359715 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -9.695359715 + 1 Combine like terms: -1 + 1 = 0 0 + v = -9.695359715 + 1 v = -9.695359715 + 1 Combine like terms: -9.695359715 + 1 = -8.695359715 v = -8.695359715 Simplifying v = -8.695359715Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.695359715, -8.695359715}
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