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Simplifying x(x + 0.1) = 0.8 Reorder the terms: x(0.1 + x) = 0.8 (0.1 * x + x * x) = 0.8 (0.1x + x2) = 0.8 Solving 0.1x + x2 = 0.8 Solving for variable 'x'. Reorder the terms: -0.8 + 0.1x + x2 = 0.8 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 -0.8 + 0.1x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.1x + 0.8 + x2 = 0.0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.1x + x2 = 0.0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.1x + x2 = 0.0 + 0.8 0.1x + x2 = 0.0 + 0.8 Combine like terms: 0.0 + 0.8 = 0.8 0.1x + x2 = 0.8 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.8 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.8 + 0.0025 Combine like terms: 0.8 + 0.0025 = 0.8025 0.0025 + 0.1x + x2 = 0.8025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.8025 Calculate the square root of the right side: 0.895823643 Break this problem into two subproblems by setting (x + 0.05) equal to 0.895823643 and -0.895823643.Subproblem 1
x + 0.05 = 0.895823643 Simplifying x + 0.05 = 0.895823643 Reorder the terms: 0.05 + x = 0.895823643 Solving 0.05 + x = 0.895823643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.895823643 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.895823643 + -0.05 x = 0.895823643 + -0.05 Combine like terms: 0.895823643 + -0.05 = 0.845823643 x = 0.845823643 Simplifying x = 0.845823643Subproblem 2
x + 0.05 = -0.895823643 Simplifying x + 0.05 = -0.895823643 Reorder the terms: 0.05 + x = -0.895823643 Solving 0.05 + x = -0.895823643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.895823643 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.895823643 + -0.05 x = -0.895823643 + -0.05 Combine like terms: -0.895823643 + -0.05 = -0.945823643 x = -0.945823643 Simplifying x = -0.945823643Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.845823643, -0.945823643}
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