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Simplifying (x + 1) * x = 231 Reorder the terms: (1 + x) * x = 231 Reorder the terms for easier multiplication: x(1 + x) = 231 (1 * x + x * x) = 231 (1x + x2) = 231 Solving 1x + x2 = 231 Solving for variable 'x'. Reorder the terms: -231 + 1x + x2 = 231 + -231 Combine like terms: 231 + -231 = 0 -231 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '231' to each side of the equation. -231 + 1x + 231 + x2 = 0 + 231 Reorder the terms: -231 + 231 + 1x + x2 = 0 + 231 Combine like terms: -231 + 231 = 0 0 + 1x + x2 = 0 + 231 1x + x2 = 0 + 231 Combine like terms: 0 + 231 = 231 1x + x2 = 231 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 231 + 0.25 Reorder the terms: 0.25 + x + x2 = 231 + 0.25 Combine like terms: 231 + 0.25 = 231.25 0.25 + x + x2 = 231.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 231.25 Calculate the square root of the right side: 15.206906326 Break this problem into two subproblems by setting (x + 0.5) equal to 15.206906326 and -15.206906326.Subproblem 1
x + 0.5 = 15.206906326 Simplifying x + 0.5 = 15.206906326 Reorder the terms: 0.5 + x = 15.206906326 Solving 0.5 + x = 15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 15.206906326 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.206906326 + -0.5 x = 15.206906326 + -0.5 Combine like terms: 15.206906326 + -0.5 = 14.706906326 x = 14.706906326 Simplifying x = 14.706906326Subproblem 2
x + 0.5 = -15.206906326 Simplifying x + 0.5 = -15.206906326 Reorder the terms: 0.5 + x = -15.206906326 Solving 0.5 + x = -15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -15.206906326 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.206906326 + -0.5 x = -15.206906326 + -0.5 Combine like terms: -15.206906326 + -0.5 = -15.706906326 x = -15.706906326 Simplifying x = -15.706906326Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.706906326, -15.706906326}
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