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Simplifying 2 = x(x + 0.1) Reorder the terms: 2 = x(0.1 + x) 2 = (0.1 * x + x * x) 2 = (0.1x + x2) Solving 2 = 0.1x + x2 Solving for variable 'x'. Reorder the terms: 2 + -0.1x + -1x2 = 0.1x + -0.1x + x2 + -1x2 Combine like terms: 0.1x + -0.1x = 0.0 2 + -0.1x + -1x2 = 0.0 + x2 + -1x2 2 + -0.1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2 + -0.1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 0.1x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.1x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.1x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.1x + x2 = 0 + 2 0.1x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.1x + x2 = 2 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 = 2 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 2 + 0.0025 Combine like terms: 2 + 0.0025 = 2.0025 0.0025 + 0.1x + x2 = 2.0025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (x + 0.05) equal to 1.41509717 and -1.41509717.Subproblem 1
x + 0.05 = 1.41509717 Simplifying x + 0.05 = 1.41509717 Reorder the terms: 0.05 + x = 1.41509717 Solving 0.05 + x = 1.41509717 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 = 1.41509717 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 1.41509717 + -0.05 x = 1.41509717 + -0.05 Combine like terms: 1.41509717 + -0.05 = 1.36509717 x = 1.36509717 Simplifying x = 1.36509717Subproblem 2
x + 0.05 = -1.41509717 Simplifying x + 0.05 = -1.41509717 Reorder the terms: 0.05 + x = -1.41509717 Solving 0.05 + x = -1.41509717 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 = -1.41509717 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -1.41509717 + -0.05 x = -1.41509717 + -0.05 Combine like terms: -1.41509717 + -0.05 = -1.46509717 x = -1.46509717 Simplifying x = -1.46509717Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.36509717, -1.46509717}
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