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Simplifying x2 + -2.0375x + 0.09 = 0 Reorder the terms: 0.09 + -2.0375x + x2 = 0 Solving 0.09 + -2.0375x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.09' to each side of the equation. 0.09 + -2.0375x + -0.09 + x2 = 0 + -0.09 Reorder the terms: 0.09 + -0.09 + -2.0375x + x2 = 0 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 0.00 + -2.0375x + x2 = 0 + -0.09 -2.0375x + x2 = 0 + -0.09 Combine like terms: 0 + -0.09 = -0.09 -2.0375x + x2 = -0.09 The x term is -2.0375x. Take half its coefficient (-1.01875). Square it (1.037851563) and add it to both sides. Add '1.037851563' to each side of the equation. -2.0375x + 1.037851563 + x2 = -0.09 + 1.037851563 Reorder the terms: 1.037851563 + -2.0375x + x2 = -0.09 + 1.037851563 Combine like terms: -0.09 + 1.037851563 = 0.947851563 1.037851563 + -2.0375x + x2 = 0.947851563 Factor a perfect square on the left side: (x + -1.01875)(x + -1.01875) = 0.947851563 Calculate the square root of the right side: 0.973576686 Break this problem into two subproblems by setting (x + -1.01875) equal to 0.973576686 and -0.973576686.Subproblem 1
x + -1.01875 = 0.973576686 Simplifying x + -1.01875 = 0.973576686 Reorder the terms: -1.01875 + x = 0.973576686 Solving -1.01875 + x = 0.973576686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.01875' to each side of the equation. -1.01875 + 1.01875 + x = 0.973576686 + 1.01875 Combine like terms: -1.01875 + 1.01875 = 0.00000 0.00000 + x = 0.973576686 + 1.01875 x = 0.973576686 + 1.01875 Combine like terms: 0.973576686 + 1.01875 = 1.992326686 x = 1.992326686 Simplifying x = 1.992326686Subproblem 2
x + -1.01875 = -0.973576686 Simplifying x + -1.01875 = -0.973576686 Reorder the terms: -1.01875 + x = -0.973576686 Solving -1.01875 + x = -0.973576686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.01875' to each side of the equation. -1.01875 + 1.01875 + x = -0.973576686 + 1.01875 Combine like terms: -1.01875 + 1.01875 = 0.00000 0.00000 + x = -0.973576686 + 1.01875 x = -0.973576686 + 1.01875 Combine like terms: -0.973576686 + 1.01875 = 0.045173314 x = 0.045173314 Simplifying x = 0.045173314Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.992326686, 0.045173314}
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