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Simplifying x(x + 1) = 0.19 Reorder the terms: x(1 + x) = 0.19 (1 * x + x * x) = 0.19 (1x + x2) = 0.19 Solving 1x + x2 = 0.19 Solving for variable 'x'. Reorder the terms: -0.19 + 1x + x2 = 0.19 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 -0.19 + 1x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.19' to each side of the equation. -0.19 + 1x + 0.19 + x2 = 0.00 + 0.19 Reorder the terms: -0.19 + 0.19 + 1x + x2 = 0.00 + 0.19 Combine like terms: -0.19 + 0.19 = 0.00 0.00 + 1x + x2 = 0.00 + 0.19 1x + x2 = 0.00 + 0.19 Combine like terms: 0.00 + 0.19 = 0.19 1x + x2 = 0.19 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 = 0.19 + 0.25 Reorder the terms: 0.25 + x + x2 = 0.19 + 0.25 Combine like terms: 0.19 + 0.25 = 0.44 0.25 + x + x2 = 0.44 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + 0.5) equal to 0.663324958 and -0.663324958.Subproblem 1
x + 0.5 = 0.663324958 Simplifying x + 0.5 = 0.663324958 Reorder the terms: 0.5 + x = 0.663324958 Solving 0.5 + x = 0.663324958 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 = 0.663324958 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.663324958 + -0.5 x = 0.663324958 + -0.5 Combine like terms: 0.663324958 + -0.5 = 0.163324958 x = 0.163324958 Simplifying x = 0.163324958Subproblem 2
x + 0.5 = -0.663324958 Simplifying x + 0.5 = -0.663324958 Reorder the terms: 0.5 + x = -0.663324958 Solving 0.5 + x = -0.663324958 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 = -0.663324958 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.663324958 + -0.5 x = -0.663324958 + -0.5 Combine like terms: -0.663324958 + -0.5 = -1.163324958 x = -1.163324958 Simplifying x = -1.163324958Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.163324958, -1.163324958}
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