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Simplifying x2 + -0.81x + 0.048 = 0 Reorder the terms: 0.048 + -0.81x + x2 = 0 Solving 0.048 + -0.81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.048' to each side of the equation. 0.048 + -0.81x + -0.048 + x2 = 0 + -0.048 Reorder the terms: 0.048 + -0.048 + -0.81x + x2 = 0 + -0.048 Combine like terms: 0.048 + -0.048 = 0.000 0.000 + -0.81x + x2 = 0 + -0.048 -0.81x + x2 = 0 + -0.048 Combine like terms: 0 + -0.048 = -0.048 -0.81x + x2 = -0.048 The x term is -0.81x. Take half its coefficient (-0.405). Square it (0.164025) and add it to both sides. Add '0.164025' to each side of the equation. -0.81x + 0.164025 + x2 = -0.048 + 0.164025 Reorder the terms: 0.164025 + -0.81x + x2 = -0.048 + 0.164025 Combine like terms: -0.048 + 0.164025 = 0.116025 0.164025 + -0.81x + x2 = 0.116025 Factor a perfect square on the left side: (x + -0.405)(x + -0.405) = 0.116025 Calculate the square root of the right side: 0.340624427 Break this problem into two subproblems by setting (x + -0.405) equal to 0.340624427 and -0.340624427.Subproblem 1
x + -0.405 = 0.340624427 Simplifying x + -0.405 = 0.340624427 Reorder the terms: -0.405 + x = 0.340624427 Solving -0.405 + x = 0.340624427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.405' to each side of the equation. -0.405 + 0.405 + x = 0.340624427 + 0.405 Combine like terms: -0.405 + 0.405 = 0.000 0.000 + x = 0.340624427 + 0.405 x = 0.340624427 + 0.405 Combine like terms: 0.340624427 + 0.405 = 0.745624427 x = 0.745624427 Simplifying x = 0.745624427Subproblem 2
x + -0.405 = -0.340624427 Simplifying x + -0.405 = -0.340624427 Reorder the terms: -0.405 + x = -0.340624427 Solving -0.405 + x = -0.340624427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.405' to each side of the equation. -0.405 + 0.405 + x = -0.340624427 + 0.405 Combine like terms: -0.405 + 0.405 = 0.000 0.000 + x = -0.340624427 + 0.405 x = -0.340624427 + 0.405 Combine like terms: -0.340624427 + 0.405 = 0.064375573 x = 0.064375573 Simplifying x = 0.064375573Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.745624427, 0.064375573}
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