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Simplifying 2v2 = -30v + -25 Reorder the terms: 2v2 = -25 + -30v Solving 2v2 = -25 + -30v Solving for variable 'v'. Reorder the terms: 25 + 30v + 2v2 = -25 + -30v + 25 + 30v Reorder the terms: 25 + 30v + 2v2 = -25 + 25 + -30v + 30v Combine like terms: -25 + 25 = 0 25 + 30v + 2v2 = 0 + -30v + 30v 25 + 30v + 2v2 = -30v + 30v Combine like terms: -30v + 30v = 0 25 + 30v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + 15v + v2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 15v + -12.5 + v2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 15v + v2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 15v + v2 = 0 + -12.5 15v + v2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 15v + v2 = -12.5 The v term is 15v. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15v + 56.25 + v2 = -12.5 + 56.25 Reorder the terms: 56.25 + 15v + v2 = -12.5 + 56.25 Combine like terms: -12.5 + 56.25 = 43.75 56.25 + 15v + v2 = 43.75 Factor a perfect square on the left side: (v + 7.5)(v + 7.5) = 43.75 Calculate the square root of the right side: 6.614378278 Break this problem into two subproblems by setting (v + 7.5) equal to 6.614378278 and -6.614378278.Subproblem 1
v + 7.5 = 6.614378278 Simplifying v + 7.5 = 6.614378278 Reorder the terms: 7.5 + v = 6.614378278 Solving 7.5 + v = 6.614378278 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = 6.614378278 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = 6.614378278 + -7.5 v = 6.614378278 + -7.5 Combine like terms: 6.614378278 + -7.5 = -0.885621722 v = -0.885621722 Simplifying v = -0.885621722Subproblem 2
v + 7.5 = -6.614378278 Simplifying v + 7.5 = -6.614378278 Reorder the terms: 7.5 + v = -6.614378278 Solving 7.5 + v = -6.614378278 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = -6.614378278 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = -6.614378278 + -7.5 v = -6.614378278 + -7.5 Combine like terms: -6.614378278 + -7.5 = -14.114378278 v = -14.114378278 Simplifying v = -14.114378278Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.885621722, -14.114378278}
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