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Simplifying v(2v + -20) = -21 Reorder the terms: v(-20 + 2v) = -21 (-20 * v + 2v * v) = -21 (-20v + 2v2) = -21 Solving -20v + 2v2 = -21 Solving for variable 'v'. Reorder the terms: 21 + -20v + 2v2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -20v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + -10v + v2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -10v + -10.5 + v2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -10v + v2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -10v + v2 = 0 + -10.5 -10v + v2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -10v + v2 = -10.5 The v term is -10v. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10v + 25 + v2 = -10.5 + 25 Reorder the terms: 25 + -10v + v2 = -10.5 + 25 Combine like terms: -10.5 + 25 = 14.5 25 + -10v + v2 = 14.5 Factor a perfect square on the left side: (v + -5)(v + -5) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (v + -5) equal to 3.807886553 and -3.807886553.Subproblem 1
v + -5 = 3.807886553 Simplifying v + -5 = 3.807886553 Reorder the terms: -5 + v = 3.807886553 Solving -5 + v = 3.807886553 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = 3.807886553 + 5 Combine like terms: -5 + 5 = 0 0 + v = 3.807886553 + 5 v = 3.807886553 + 5 Combine like terms: 3.807886553 + 5 = 8.807886553 v = 8.807886553 Simplifying v = 8.807886553Subproblem 2
v + -5 = -3.807886553 Simplifying v + -5 = -3.807886553 Reorder the terms: -5 + v = -3.807886553 Solving -5 + v = -3.807886553 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = -3.807886553 + 5 Combine like terms: -5 + 5 = 0 0 + v = -3.807886553 + 5 v = -3.807886553 + 5 Combine like terms: -3.807886553 + 5 = 1.192113447 v = 1.192113447 Simplifying v = 1.192113447Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.807886553, 1.192113447}
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