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Simplifying 2 * 10 + -16 = x(x + 0.1) Multiply 2 * 10 20 + -16 = x(x + 0.1) Combine like terms: 20 + -16 = 4 4 = x(x + 0.1) Reorder the terms: 4 = x(0.1 + x) 4 = (0.1 * x + x * x) 4 = (0.1x + x2) Solving 4 = 0.1x + x2 Solving for variable 'x'. Reorder the terms: 4 + -0.1x + -1x2 = 0.1x + -0.1x + x2 + -1x2 Combine like terms: 0.1x + -0.1x = 0.0 4 + -0.1x + -1x2 = 0.0 + x2 + -1x2 4 + -0.1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + -0.1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 0.1x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.1x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.1x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.1x + x2 = 0 + 4 0.1x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.1x + x2 = 4 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 = 4 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 4 + 0.0025 Combine like terms: 4 + 0.0025 = 4.0025 0.0025 + 0.1x + x2 = 4.0025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 4.0025 Calculate the square root of the right side: 2.000624902 Break this problem into two subproblems by setting (x + 0.05) equal to 2.000624902 and -2.000624902.Subproblem 1
x + 0.05 = 2.000624902 Simplifying x + 0.05 = 2.000624902 Reorder the terms: 0.05 + x = 2.000624902 Solving 0.05 + x = 2.000624902 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 = 2.000624902 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 2.000624902 + -0.05 x = 2.000624902 + -0.05 Combine like terms: 2.000624902 + -0.05 = 1.950624902 x = 1.950624902 Simplifying x = 1.950624902Subproblem 2
x + 0.05 = -2.000624902 Simplifying x + 0.05 = -2.000624902 Reorder the terms: 0.05 + x = -2.000624902 Solving 0.05 + x = -2.000624902 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 = -2.000624902 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -2.000624902 + -0.05 x = -2.000624902 + -0.05 Combine like terms: -2.000624902 + -0.05 = -2.050624902 x = -2.050624902 Simplifying x = -2.050624902Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.950624902, -2.050624902}
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