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Simplifying x * x + 1 = 11 + x + 1 + x Multiply x * x x2 + 1 = 11 + x + 1 + x Reorder the terms: 1 + x2 = 11 + x + 1 + x Reorder the terms: 1 + x2 = 11 + 1 + x + x Combine like terms: 11 + 1 = 12 1 + x2 = 12 + x + x Combine like terms: x + x = 2x 1 + x2 = 12 + 2x Solving 1 + x2 = 12 + 2x Solving for variable 'x'. Reorder the terms: 1 + -12 + -2x + x2 = 12 + 2x + -12 + -2x Combine like terms: 1 + -12 = -11 -11 + -2x + x2 = 12 + 2x + -12 + -2x Reorder the terms: -11 + -2x + x2 = 12 + -12 + 2x + -2x Combine like terms: 12 + -12 = 0 -11 + -2x + x2 = 0 + 2x + -2x -11 + -2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -11 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -2x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -2x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2x + x2 = 0 + 11 -2x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2x + x2 = 11 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 11 + 1 Reorder the terms: 1 + -2x + x2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + -2x + x2 = 12 Factor a perfect square on the left side: (x + -1)(x + -1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -1) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -1 = 3.464101615 Simplifying x + -1 = 3.464101615 Reorder the terms: -1 + x = 3.464101615 Solving -1 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.464101615 + 1 x = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 x = 4.464101615 Simplifying x = 4.464101615Subproblem 2
x + -1 = -3.464101615 Simplifying x + -1 = -3.464101615 Reorder the terms: -1 + x = -3.464101615 Solving -1 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.464101615 + 1 x = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 x = -2.464101615 Simplifying x = -2.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.464101615, -2.464101615}
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