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Simplifying (x + 1)(x + 1) = 103 Reorder the terms: (1 + x)(x + 1) = 103 Reorder the terms: (1 + x)(1 + x) = 103 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) = 103 ((1 * 1 + x * 1) + x(1 + x)) = 103 ((1 + 1x) + x(1 + x)) = 103 (1 + 1x + (1 * x + x * x)) = 103 (1 + 1x + (1x + x2)) = 103 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) = 103 Solving 1 + 2x + x2 = 103 Solving for variable 'x'. Reorder the terms: 1 + -103 + 2x + x2 = 103 + -103 Combine like terms: 1 + -103 = -102 -102 + 2x + x2 = 103 + -103 Combine like terms: 103 + -103 = 0 -102 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 2x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 2x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 2x + x2 = 0 + 102 2x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 2x + x2 = 102 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 = 102 + 1 Reorder the terms: 1 + 2x + x2 = 102 + 1 Combine like terms: 102 + 1 = 103 1 + 2x + x2 = 103 Factor a perfect square on the left side: (x + 1)(x + 1) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + 1) equal to 10.148891565 and -10.148891565.Subproblem 1
x + 1 = 10.148891565 Simplifying x + 1 = 10.148891565 Reorder the terms: 1 + x = 10.148891565 Solving 1 + x = 10.148891565 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 = 10.148891565 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.148891565 + -1 x = 10.148891565 + -1 Combine like terms: 10.148891565 + -1 = 9.148891565 x = 9.148891565 Simplifying x = 9.148891565Subproblem 2
x + 1 = -10.148891565 Simplifying x + 1 = -10.148891565 Reorder the terms: 1 + x = -10.148891565 Solving 1 + x = -10.148891565 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 = -10.148891565 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.148891565 + -1 x = -10.148891565 + -1 Combine like terms: -10.148891565 + -1 = -11.148891565 x = -11.148891565 Simplifying x = -11.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.148891565, -11.148891565}
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