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Simplifying x2 + -11 = 4x Reorder the terms: -11 + x2 = 4x Solving -11 + x2 = 4x Solving for variable 'x'. Reorder the terms: -11 + -4x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -11 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -4x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -4x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4x + x2 = 0 + 11 -4x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4x + x2 = 11 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 11 + 4 Reorder the terms: 4 + -4x + x2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + -4x + x2 = 15 Factor a perfect square on the left side: (x + -2)(x + -2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -2) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -2 = 3.872983346 Simplifying x + -2 = 3.872983346 Reorder the terms: -2 + x = 3.872983346 Solving -2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.872983346 + 2 x = 3.872983346 + 2 Combine like terms: 3.872983346 + 2 = 5.872983346 x = 5.872983346 Simplifying x = 5.872983346Subproblem 2
x + -2 = -3.872983346 Simplifying x + -2 = -3.872983346 Reorder the terms: -2 + x = -3.872983346 Solving -2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.872983346 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.872983346 + 2 x = -3.872983346 + 2 Combine like terms: -3.872983346 + 2 = -1.872983346 x = -1.872983346 Simplifying x = -1.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.872983346, -1.872983346}
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