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Simplifying -2v2 + 52v + 46 = 0 Reorder the terms: 46 + 52v + -2v2 = 0 Solving 46 + 52v + -2v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(23 + 26v + -1v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + 26v + -1v2)' equal to zero and attempt to solve: Simplifying 23 + 26v + -1v2 = 0 Solving 23 + 26v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + -26v + v2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -26v + 23 + v2 = 0 + 23 Reorder the terms: -23 + 23 + -26v + v2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -26v + v2 = 0 + 23 -26v + v2 = 0 + 23 Combine like terms: 0 + 23 = 23 -26v + v2 = 23 The v term is -26v. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26v + 169 + v2 = 23 + 169 Reorder the terms: 169 + -26v + v2 = 23 + 169 Combine like terms: 23 + 169 = 192 169 + -26v + v2 = 192 Factor a perfect square on the left side: (v + -13)(v + -13) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (v + -13) equal to 13.856406461 and -13.856406461.Subproblem 1
v + -13 = 13.856406461 Simplifying v + -13 = 13.856406461 Reorder the terms: -13 + v = 13.856406461 Solving -13 + v = 13.856406461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = 13.856406461 + 13 Combine like terms: -13 + 13 = 0 0 + v = 13.856406461 + 13 v = 13.856406461 + 13 Combine like terms: 13.856406461 + 13 = 26.856406461 v = 26.856406461 Simplifying v = 26.856406461Subproblem 2
v + -13 = -13.856406461 Simplifying v + -13 = -13.856406461 Reorder the terms: -13 + v = -13.856406461 Solving -13 + v = -13.856406461 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = -13.856406461 + 13 Combine like terms: -13 + 13 = 0 0 + v = -13.856406461 + 13 v = -13.856406461 + 13 Combine like terms: -13.856406461 + 13 = -0.856406461 v = -0.856406461 Simplifying v = -0.856406461Solution
The solution to the problem is based on the solutions from the subproblems. v = {26.856406461, -0.856406461}Solution
v = {26.856406461, -0.856406461}
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