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Simplifying -4.905x2 + -1.11x + 0.8 = 0 Reorder the terms: 0.8 + -1.11x + -4.905x2 = 0 Solving 0.8 + -1.11x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -0.1630988787 + 0.2262996942x + x2 = 0 Move the constant term to the right: Add '0.1630988787' to each side of the equation. -0.1630988787 + 0.2262996942x + 0.1630988787 + x2 = 0 + 0.1630988787 Reorder the terms: -0.1630988787 + 0.1630988787 + 0.2262996942x + x2 = 0 + 0.1630988787 Combine like terms: -0.1630988787 + 0.1630988787 = 0.0000000000 0.0000000000 + 0.2262996942x + x2 = 0 + 0.1630988787 0.2262996942x + x2 = 0 + 0.1630988787 Combine like terms: 0 + 0.1630988787 = 0.1630988787 0.2262996942x + x2 = 0.1630988787 The x term is 0.2262996942x. Take half its coefficient (0.1131498471). Square it (0.01280288790) and add it to both sides. Add '0.01280288790' to each side of the equation. 0.2262996942x + 0.01280288790 + x2 = 0.1630988787 + 0.01280288790 Reorder the terms: 0.01280288790 + 0.2262996942x + x2 = 0.1630988787 + 0.01280288790 Combine like terms: 0.1630988787 + 0.01280288790 = 0.1759017666 0.01280288790 + 0.2262996942x + x2 = 0.1759017666 Factor a perfect square on the left side: (x + 0.1131498471)(x + 0.1131498471) = 0.1759017666 Calculate the square root of the right side: 0.419406446 Break this problem into two subproblems by setting (x + 0.1131498471) equal to 0.419406446 and -0.419406446.Subproblem 1
x + 0.1131498471 = 0.419406446 Simplifying x + 0.1131498471 = 0.419406446 Reorder the terms: 0.1131498471 + x = 0.419406446 Solving 0.1131498471 + x = 0.419406446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1131498471' to each side of the equation. 0.1131498471 + -0.1131498471 + x = 0.419406446 + -0.1131498471 Combine like terms: 0.1131498471 + -0.1131498471 = 0.0000000000 0.0000000000 + x = 0.419406446 + -0.1131498471 x = 0.419406446 + -0.1131498471 Combine like terms: 0.419406446 + -0.1131498471 = 0.3062565989 x = 0.3062565989 Simplifying x = 0.3062565989Subproblem 2
x + 0.1131498471 = -0.419406446 Simplifying x + 0.1131498471 = -0.419406446 Reorder the terms: 0.1131498471 + x = -0.419406446 Solving 0.1131498471 + x = -0.419406446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1131498471' to each side of the equation. 0.1131498471 + -0.1131498471 + x = -0.419406446 + -0.1131498471 Combine like terms: 0.1131498471 + -0.1131498471 = 0.0000000000 0.0000000000 + x = -0.419406446 + -0.1131498471 x = -0.419406446 + -0.1131498471 Combine like terms: -0.419406446 + -0.1131498471 = -0.5325562931 x = -0.5325562931 Simplifying x = -0.5325562931Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3062565989, -0.5325562931}
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