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Simplifying x2 + 0.095x = 0.0000000028 Reorder the terms: 0.095x + x2 = 0.0000000028 Solving 0.095x + x2 = 0.0000000028 Solving for variable 'x'. Reorder the terms: -0.0000000028 + 0.095x + x2 = 0.0000000028 + -0.0000000028 Combine like terms: 0.0000000028 + -0.0000000028 = 0.0000000000 -0.0000000028 + 0.095x + x2 = 0.0000000000 Begin completing the square. Move the constant term to the right: Add '0.0000000028' to each side of the equation. -0.0000000028 + 0.095x + 0.0000000028 + x2 = 0.0000000000 + 0.0000000028 Reorder the terms: -0.0000000028 + 0.0000000028 + 0.095x + x2 = 0.0000000000 + 0.0000000028 Combine like terms: -0.0000000028 + 0.0000000028 = 0.0000000000 0.0000000000 + 0.095x + x2 = 0.0000000000 + 0.0000000028 0.095x + x2 = 0.0000000000 + 0.0000000028 Combine like terms: 0.0000000000 + 0.0000000028 = 0.0000000028 0.095x + x2 = 0.0000000028 The x term is 0.095x. Take half its coefficient (0.0475). Square it (0.00225625) and add it to both sides. Add '0.00225625' to each side of the equation. 0.095x + 0.00225625 + x2 = 0.0000000028 + 0.00225625 Reorder the terms: 0.00225625 + 0.095x + x2 = 0.0000000028 + 0.00225625 Combine like terms: 0.0000000028 + 0.00225625 = 0.0022562528 0.00225625 + 0.095x + x2 = 0.0022562528 Factor a perfect square on the left side: (x + 0.0475)(x + 0.0475) = 0.0022562528 Calculate the square root of the right side: 0.047500029 Break this problem into two subproblems by setting (x + 0.0475) equal to 0.047500029 and -0.047500029.Subproblem 1
x + 0.0475 = 0.047500029 Simplifying x + 0.0475 = 0.047500029 Reorder the terms: 0.0475 + x = 0.047500029 Solving 0.0475 + x = 0.047500029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0475' to each side of the equation. 0.0475 + -0.0475 + x = 0.047500029 + -0.0475 Combine like terms: 0.0475 + -0.0475 = 0.0000 0.0000 + x = 0.047500029 + -0.0475 x = 0.047500029 + -0.0475 Combine like terms: 0.047500029 + -0.0475 = 0.000000029 x = 0.000000029 Simplifying x = 0.000000029Subproblem 2
x + 0.0475 = -0.047500029 Simplifying x + 0.0475 = -0.047500029 Reorder the terms: 0.0475 + x = -0.047500029 Solving 0.0475 + x = -0.047500029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0475' to each side of the equation. 0.0475 + -0.0475 + x = -0.047500029 + -0.0475 Combine like terms: 0.0475 + -0.0475 = 0.0000 0.0000 + x = -0.047500029 + -0.0475 x = -0.047500029 + -0.0475 Combine like terms: -0.047500029 + -0.0475 = -0.095000029 x = -0.095000029 Simplifying x = -0.095000029Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000000029, -0.095000029}
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