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Simplifying 3v2 + -72v = 141 Reorder the terms: -72v + 3v2 = 141 Solving -72v + 3v2 = 141 Solving for variable 'v'. Reorder the terms: -141 + -72v + 3v2 = 141 + -141 Combine like terms: 141 + -141 = 0 -141 + -72v + 3v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-47 + -24v + v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-47 + -24v + v2)' equal to zero and attempt to solve: Simplifying -47 + -24v + v2 = 0 Solving -47 + -24v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -24v + 47 + v2 = 0 + 47 Reorder the terms: -47 + 47 + -24v + v2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -24v + v2 = 0 + 47 -24v + v2 = 0 + 47 Combine like terms: 0 + 47 = 47 -24v + v2 = 47 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 = 47 + 144 Reorder the terms: 144 + -24v + v2 = 47 + 144 Combine like terms: 47 + 144 = 191 144 + -24v + v2 = 191 Factor a perfect square on the left side: (v + -12)(v + -12) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (v + -12) equal to 13.820274961 and -13.820274961.Subproblem 1
v + -12 = 13.820274961 Simplifying v + -12 = 13.820274961 Reorder the terms: -12 + v = 13.820274961 Solving -12 + v = 13.820274961 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 = 13.820274961 + 12 Combine like terms: -12 + 12 = 0 0 + v = 13.820274961 + 12 v = 13.820274961 + 12 Combine like terms: 13.820274961 + 12 = 25.820274961 v = 25.820274961 Simplifying v = 25.820274961Subproblem 2
v + -12 = -13.820274961 Simplifying v + -12 = -13.820274961 Reorder the terms: -12 + v = -13.820274961 Solving -12 + v = -13.820274961 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 = -13.820274961 + 12 Combine like terms: -12 + 12 = 0 0 + v = -13.820274961 + 12 v = -13.820274961 + 12 Combine like terms: -13.820274961 + 12 = -1.820274961 v = -1.820274961 Simplifying v = -1.820274961Solution
The solution to the problem is based on the solutions from the subproblems. v = {25.820274961, -1.820274961}Solution
v = {25.820274961, -1.820274961}
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