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Simplifying 5v2 + -10v = 21 Reorder the terms: -10v + 5v2 = 21 Solving -10v + 5v2 = 21 Solving for variable 'v'. Reorder the terms: -21 + -10v + 5v2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -10v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -2v + v2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -2v + 4.2 + v2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -2v + v2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -2v + v2 = 0 + 4.2 -2v + v2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -2v + v2 = 4.2 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 4.2 + 1 Reorder the terms: 1 + -2v + v2 = 4.2 + 1 Combine like terms: 4.2 + 1 = 5.2 1 + -2v + v2 = 5.2 Factor a perfect square on the left side: (v + -1)(v + -1) = 5.2 Calculate the square root of the right side: 2.28035085 Break this problem into two subproblems by setting (v + -1) equal to 2.28035085 and -2.28035085.Subproblem 1
v + -1 = 2.28035085 Simplifying v + -1 = 2.28035085 Reorder the terms: -1 + v = 2.28035085 Solving -1 + v = 2.28035085 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 2.28035085 + 1 Combine like terms: -1 + 1 = 0 0 + v = 2.28035085 + 1 v = 2.28035085 + 1 Combine like terms: 2.28035085 + 1 = 3.28035085 v = 3.28035085 Simplifying v = 3.28035085Subproblem 2
v + -1 = -2.28035085 Simplifying v + -1 = -2.28035085 Reorder the terms: -1 + v = -2.28035085 Solving -1 + v = -2.28035085 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -2.28035085 + 1 Combine like terms: -1 + 1 = 0 0 + v = -2.28035085 + 1 v = -2.28035085 + 1 Combine like terms: -2.28035085 + 1 = -1.28035085 v = -1.28035085 Simplifying v = -1.28035085Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.28035085, -1.28035085}
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