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Simplifying 4v2 + 20v + -21 = 0 Reorder the terms: -21 + 20v + 4v2 = 0 Solving -21 + 20v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 5v + v2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 5v + 5.25 + v2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 5v + v2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 5v + v2 = 0 + 5.25 5v + v2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 5v + v2 = 5.25 The v term is 5v. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5v + 6.25 + v2 = 5.25 + 6.25 Reorder the terms: 6.25 + 5v + v2 = 5.25 + 6.25 Combine like terms: 5.25 + 6.25 = 11.5 6.25 + 5v + v2 = 11.5 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (v + 2.5) equal to 3.391164992 and -3.391164992.Subproblem 1
v + 2.5 = 3.391164992 Simplifying v + 2.5 = 3.391164992 Reorder the terms: 2.5 + v = 3.391164992 Solving 2.5 + v = 3.391164992 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = 3.391164992 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = 3.391164992 + -2.5 v = 3.391164992 + -2.5 Combine like terms: 3.391164992 + -2.5 = 0.891164992 v = 0.891164992 Simplifying v = 0.891164992Subproblem 2
v + 2.5 = -3.391164992 Simplifying v + 2.5 = -3.391164992 Reorder the terms: 2.5 + v = -3.391164992 Solving 2.5 + v = -3.391164992 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = -3.391164992 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = -3.391164992 + -2.5 v = -3.391164992 + -2.5 Combine like terms: -3.391164992 + -2.5 = -5.891164992 v = -5.891164992 Simplifying v = -5.891164992Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.891164992, -5.891164992}
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