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Simplifying x2 + -1(0.1x) + -1(0.05) = 0 Remove parenthesis around (0.1x) x2 + -1 * 0.1x + -1(0.05) = 0 Multiply -1 * 0.1 x2 + -0.1x + -1(0.05) = 0 Multiply -1 * 0.05 x2 + -0.1x + -0.05 = 0 Reorder the terms: -0.05 + -0.1x + x2 = 0 Solving -0.05 + -0.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + -0.1x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + -0.1x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + -0.1x + x2 = 0 + 0.05 -0.1x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 -0.1x + x2 = 0.05 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 = 0.05 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.05 + 0.0025 Combine like terms: 0.05 + 0.0025 = 0.0525 0.0025 + -0.1x + x2 = 0.0525 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.0525 Calculate the square root of the right side: 0.229128785 Break this problem into two subproblems by setting (x + -0.05) equal to 0.229128785 and -0.229128785.Subproblem 1
x + -0.05 = 0.229128785 Simplifying x + -0.05 = 0.229128785 Reorder the terms: -0.05 + x = 0.229128785 Solving -0.05 + x = 0.229128785 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 = 0.229128785 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.229128785 + 0.05 x = 0.229128785 + 0.05 Combine like terms: 0.229128785 + 0.05 = 0.279128785 x = 0.279128785 Simplifying x = 0.279128785Subproblem 2
x + -0.05 = -0.229128785 Simplifying x + -0.05 = -0.229128785 Reorder the terms: -0.05 + x = -0.229128785 Solving -0.05 + x = -0.229128785 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 = -0.229128785 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.229128785 + 0.05 x = -0.229128785 + 0.05 Combine like terms: -0.229128785 + 0.05 = -0.179128785 x = -0.179128785 Simplifying x = -0.179128785Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.279128785, -0.179128785}
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