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Simplifying v2 + 4v + -90 = -4 Reorder the terms: -90 + 4v + v2 = -4 Solving -90 + 4v + v2 = -4 Solving for variable 'v'. Reorder the terms: -90 + 4 + 4v + v2 = -4 + 4 Combine like terms: -90 + 4 = -86 -86 + 4v + v2 = -4 + 4 Combine like terms: -4 + 4 = 0 -86 + 4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + 4v + 86 + v2 = 0 + 86 Reorder the terms: -86 + 86 + 4v + v2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 4v + v2 = 0 + 86 4v + v2 = 0 + 86 Combine like terms: 0 + 86 = 86 4v + v2 = 86 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 = 86 + 4 Reorder the terms: 4 + 4v + v2 = 86 + 4 Combine like terms: 86 + 4 = 90 4 + 4v + v2 = 90 Factor a perfect square on the left side: (v + 2)(v + 2) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (v + 2) equal to 9.486832981 and -9.486832981.Subproblem 1
v + 2 = 9.486832981 Simplifying v + 2 = 9.486832981 Reorder the terms: 2 + v = 9.486832981 Solving 2 + v = 9.486832981 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 = 9.486832981 + -2 Combine like terms: 2 + -2 = 0 0 + v = 9.486832981 + -2 v = 9.486832981 + -2 Combine like terms: 9.486832981 + -2 = 7.486832981 v = 7.486832981 Simplifying v = 7.486832981Subproblem 2
v + 2 = -9.486832981 Simplifying v + 2 = -9.486832981 Reorder the terms: 2 + v = -9.486832981 Solving 2 + v = -9.486832981 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 = -9.486832981 + -2 Combine like terms: 2 + -2 = 0 0 + v = -9.486832981 + -2 v = -9.486832981 + -2 Combine like terms: -9.486832981 + -2 = -11.486832981 v = -11.486832981 Simplifying v = -11.486832981Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.486832981, -11.486832981}
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