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Simplifying 4x2 + -2.2x + 0.0024 = 0 Reorder the terms: 0.0024 + -2.2x + 4x2 = 0 Solving 0.0024 + -2.2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.0006 + -0.55x + x2 = 0 Move the constant term to the right: Add '-0.0006' to each side of the equation. 0.0006 + -0.55x + -0.0006 + x2 = 0 + -0.0006 Reorder the terms: 0.0006 + -0.0006 + -0.55x + x2 = 0 + -0.0006 Combine like terms: 0.0006 + -0.0006 = 0.0000 0.0000 + -0.55x + x2 = 0 + -0.0006 -0.55x + x2 = 0 + -0.0006 Combine like terms: 0 + -0.0006 = -0.0006 -0.55x + x2 = -0.0006 The x term is -0.55x. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x + 0.075625 + x2 = -0.0006 + 0.075625 Reorder the terms: 0.075625 + -0.55x + x2 = -0.0006 + 0.075625 Combine like terms: -0.0006 + 0.075625 = 0.075025 0.075625 + -0.55x + x2 = 0.075025 Factor a perfect square on the left side: (x + -0.275)(x + -0.275) = 0.075025 Calculate the square root of the right side: 0.273906918 Break this problem into two subproblems by setting (x + -0.275) equal to 0.273906918 and -0.273906918.Subproblem 1
x + -0.275 = 0.273906918 Simplifying x + -0.275 = 0.273906918 Reorder the terms: -0.275 + x = 0.273906918 Solving -0.275 + x = 0.273906918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = 0.273906918 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = 0.273906918 + 0.275 x = 0.273906918 + 0.275 Combine like terms: 0.273906918 + 0.275 = 0.548906918 x = 0.548906918 Simplifying x = 0.548906918Subproblem 2
x + -0.275 = -0.273906918 Simplifying x + -0.275 = -0.273906918 Reorder the terms: -0.275 + x = -0.273906918 Solving -0.275 + x = -0.273906918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = -0.273906918 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = -0.273906918 + 0.275 x = -0.273906918 + 0.275 Combine like terms: -0.273906918 + 0.275 = 0.001093082 x = 0.001093082 Simplifying x = 0.001093082Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.548906918, 0.001093082}
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