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Simplifying v2 + -24v + -11 = 0 Reorder the terms: -11 + -24v + v2 = 0 Solving -11 + -24v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -24v + 11 + v2 = 0 + 11 Reorder the terms: -11 + 11 + -24v + v2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -24v + v2 = 0 + 11 -24v + v2 = 0 + 11 Combine like terms: 0 + 11 = 11 -24v + v2 = 11 The v term is -24v. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24v + 144 + v2 = 11 + 144 Reorder the terms: 144 + -24v + v2 = 11 + 144 Combine like terms: 11 + 144 = 155 144 + -24v + v2 = 155 Factor a perfect square on the left side: (v + -12)(v + -12) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (v + -12) equal to 12.449899598 and -12.449899598.Subproblem 1
v + -12 = 12.449899598 Simplifying v + -12 = 12.449899598 Reorder the terms: -12 + v = 12.449899598 Solving -12 + v = 12.449899598 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + v = 12.449899598 + 12 Combine like terms: -12 + 12 = 0 0 + v = 12.449899598 + 12 v = 12.449899598 + 12 Combine like terms: 12.449899598 + 12 = 24.449899598 v = 24.449899598 Simplifying v = 24.449899598Subproblem 2
v + -12 = -12.449899598 Simplifying v + -12 = -12.449899598 Reorder the terms: -12 + v = -12.449899598 Solving -12 + v = -12.449899598 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + v = -12.449899598 + 12 Combine like terms: -12 + 12 = 0 0 + v = -12.449899598 + 12 v = -12.449899598 + 12 Combine like terms: -12.449899598 + 12 = -0.449899598 v = -0.449899598 Simplifying v = -0.449899598Solution
The solution to the problem is based on the solutions from the subproblems. v = {24.449899598, -0.449899598}
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