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Simplifying 3v2 + -60v = -141 Reorder the terms: -60v + 3v2 = -141 Solving -60v + 3v2 = -141 Solving for variable 'v'. Reorder the terms: 141 + -60v + 3v2 = -141 + 141 Combine like terms: -141 + 141 = 0 141 + -60v + 3v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(47 + -20v + v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(47 + -20v + v2)' equal to zero and attempt to solve: Simplifying 47 + -20v + v2 = 0 Solving 47 + -20v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -20v + -47 + v2 = 0 + -47 Reorder the terms: 47 + -47 + -20v + v2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -20v + v2 = 0 + -47 -20v + v2 = 0 + -47 Combine like terms: 0 + -47 = -47 -20v + v2 = -47 The v term is -20v. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20v + 100 + v2 = -47 + 100 Reorder the terms: 100 + -20v + v2 = -47 + 100 Combine like terms: -47 + 100 = 53 100 + -20v + v2 = 53 Factor a perfect square on the left side: (v + -10)(v + -10) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (v + -10) equal to 7.280109889 and -7.280109889.Subproblem 1
v + -10 = 7.280109889 Simplifying v + -10 = 7.280109889 Reorder the terms: -10 + v = 7.280109889 Solving -10 + v = 7.280109889 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + v = 7.280109889 + 10 Combine like terms: -10 + 10 = 0 0 + v = 7.280109889 + 10 v = 7.280109889 + 10 Combine like terms: 7.280109889 + 10 = 17.280109889 v = 17.280109889 Simplifying v = 17.280109889Subproblem 2
v + -10 = -7.280109889 Simplifying v + -10 = -7.280109889 Reorder the terms: -10 + v = -7.280109889 Solving -10 + v = -7.280109889 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + v = -7.280109889 + 10 Combine like terms: -10 + 10 = 0 0 + v = -7.280109889 + 10 v = -7.280109889 + 10 Combine like terms: -7.280109889 + 10 = 2.719890111 v = 2.719890111 Simplifying v = 2.719890111Solution
The solution to the problem is based on the solutions from the subproblems. v = {17.280109889, 2.719890111}Solution
v = {17.280109889, 2.719890111}
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