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Simplifying (1 + x)(1 + x) = 1.23 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) = 1.23 ((1 * 1 + x * 1) + x(1 + x)) = 1.23 ((1 + 1x) + x(1 + x)) = 1.23 (1 + 1x + (1 * x + x * x)) = 1.23 (1 + 1x + (1x + x2)) = 1.23 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) = 1.23 Solving 1 + 2x + x2 = 1.23 Solving for variable 'x'. Reorder the terms: 1 + -1.23 + 2x + x2 = 1.23 + -1.23 Combine like terms: 1 + -1.23 = -0.23 -0.23 + 2x + x2 = 1.23 + -1.23 Combine like terms: 1.23 + -1.23 = 0.00 -0.23 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.23' to each side of the equation. -0.23 + 2x + 0.23 + x2 = 0.00 + 0.23 Reorder the terms: -0.23 + 0.23 + 2x + x2 = 0.00 + 0.23 Combine like terms: -0.23 + 0.23 = 0.00 0.00 + 2x + x2 = 0.00 + 0.23 2x + x2 = 0.00 + 0.23 Combine like terms: 0.00 + 0.23 = 0.23 2x + x2 = 0.23 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 = 0.23 + 1 Reorder the terms: 1 + 2x + x2 = 0.23 + 1 Combine like terms: 0.23 + 1 = 1.23 1 + 2x + x2 = 1.23 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.23 Calculate the square root of the right side: 1.109053651 Break this problem into two subproblems by setting (x + 1) equal to 1.109053651 and -1.109053651.Subproblem 1
x + 1 = 1.109053651 Simplifying x + 1 = 1.109053651 Reorder the terms: 1 + x = 1.109053651 Solving 1 + x = 1.109053651 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 = 1.109053651 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.109053651 + -1 x = 1.109053651 + -1 Combine like terms: 1.109053651 + -1 = 0.109053651 x = 0.109053651 Simplifying x = 0.109053651Subproblem 2
x + 1 = -1.109053651 Simplifying x + 1 = -1.109053651 Reorder the terms: 1 + x = -1.109053651 Solving 1 + x = -1.109053651 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 = -1.109053651 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.109053651 + -1 x = -1.109053651 + -1 Combine like terms: -1.109053651 + -1 = -2.109053651 x = -2.109053651 Simplifying x = -2.109053651Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.109053651, -2.109053651}
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