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Simplifying -1v2 + -4v + 90 = 0 Reorder the terms: 90 + -4v + -1v2 = 0 Solving 90 + -4v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + 4v + v2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 4v + 90 + v2 = 0 + 90 Reorder the terms: -90 + 90 + 4v + v2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 4v + v2 = 0 + 90 4v + v2 = 0 + 90 Combine like terms: 0 + 90 = 90 4v + v2 = 90 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 90 + 4 Reorder the terms: 4 + 4v + v2 = 90 + 4 Combine like terms: 90 + 4 = 94 4 + 4v + v2 = 94 Factor a perfect square on the left side: (v + 2)(v + 2) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (v + 2) equal to 9.695359715 and -9.695359715.Subproblem 1
v + 2 = 9.695359715 Simplifying v + 2 = 9.695359715 Reorder the terms: 2 + v = 9.695359715 Solving 2 + v = 9.695359715 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 9.695359715 + -2 Combine like terms: 2 + -2 = 0 0 + v = 9.695359715 + -2 v = 9.695359715 + -2 Combine like terms: 9.695359715 + -2 = 7.695359715 v = 7.695359715 Simplifying v = 7.695359715Subproblem 2
v + 2 = -9.695359715 Simplifying v + 2 = -9.695359715 Reorder the terms: 2 + v = -9.695359715 Solving 2 + v = -9.695359715 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -9.695359715 + -2 Combine like terms: 2 + -2 = 0 0 + v = -9.695359715 + -2 v = -9.695359715 + -2 Combine like terms: -9.695359715 + -2 = -11.695359715 v = -11.695359715 Simplifying v = -11.695359715Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.695359715, -11.695359715}
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