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Simplifying 8v2 + -24v + 9 = 0 Reorder the terms: 9 + -24v + 8v2 = 0 Solving 9 + -24v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -3v + v2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -3v + -1.125 + v2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -3v + v2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -3v + v2 = 0 + -1.125 -3v + v2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -3v + v2 = -1.125 The v term is -3v. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3v + 2.25 + v2 = -1.125 + 2.25 Reorder the terms: 2.25 + -3v + v2 = -1.125 + 2.25 Combine like terms: -1.125 + 2.25 = 1.125 2.25 + -3v + v2 = 1.125 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (v + -1.5) equal to 1.060660172 and -1.060660172.Subproblem 1
v + -1.5 = 1.060660172 Simplifying v + -1.5 = 1.060660172 Reorder the terms: -1.5 + v = 1.060660172 Solving -1.5 + v = 1.060660172 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = 1.060660172 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = 1.060660172 + 1.5 v = 1.060660172 + 1.5 Combine like terms: 1.060660172 + 1.5 = 2.560660172 v = 2.560660172 Simplifying v = 2.560660172Subproblem 2
v + -1.5 = -1.060660172 Simplifying v + -1.5 = -1.060660172 Reorder the terms: -1.5 + v = -1.060660172 Solving -1.5 + v = -1.060660172 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = -1.060660172 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = -1.060660172 + 1.5 v = -1.060660172 + 1.5 Combine like terms: -1.060660172 + 1.5 = 0.439339828 v = 0.439339828 Simplifying v = 0.439339828Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.560660172, 0.439339828}
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