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Simplifying 45x2 + -92x + 46 = 0 Reorder the terms: 46 + -92x + 45x2 = 0 Solving 46 + -92x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 1.022222222 + -2.044444444x + x2 = 0 Move the constant term to the right: Add '-1.022222222' to each side of the equation. 1.022222222 + -2.044444444x + -1.022222222 + x2 = 0 + -1.022222222 Reorder the terms: 1.022222222 + -1.022222222 + -2.044444444x + x2 = 0 + -1.022222222 Combine like terms: 1.022222222 + -1.022222222 = 0.000000000 0.000000000 + -2.044444444x + x2 = 0 + -1.022222222 -2.044444444x + x2 = 0 + -1.022222222 Combine like terms: 0 + -1.022222222 = -1.022222222 -2.044444444x + x2 = -1.022222222 The x term is -2.044444444x. Take half its coefficient (-1.022222222). Square it (1.044938271) and add it to both sides. Add '1.044938271' to each side of the equation. -2.044444444x + 1.044938271 + x2 = -1.022222222 + 1.044938271 Reorder the terms: 1.044938271 + -2.044444444x + x2 = -1.022222222 + 1.044938271 Combine like terms: -1.022222222 + 1.044938271 = 0.022716049 1.044938271 + -2.044444444x + x2 = 0.022716049 Factor a perfect square on the left side: (x + -1.022222222)(x + -1.022222222) = 0.022716049 Calculate the square root of the right side: 0.150718443 Break this problem into two subproblems by setting (x + -1.022222222) equal to 0.150718443 and -0.150718443.Subproblem 1
x + -1.022222222 = 0.150718443 Simplifying x + -1.022222222 = 0.150718443 Reorder the terms: -1.022222222 + x = 0.150718443 Solving -1.022222222 + x = 0.150718443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.022222222' to each side of the equation. -1.022222222 + 1.022222222 + x = 0.150718443 + 1.022222222 Combine like terms: -1.022222222 + 1.022222222 = 0.000000000 0.000000000 + x = 0.150718443 + 1.022222222 x = 0.150718443 + 1.022222222 Combine like terms: 0.150718443 + 1.022222222 = 1.172940665 x = 1.172940665 Simplifying x = 1.172940665Subproblem 2
x + -1.022222222 = -0.150718443 Simplifying x + -1.022222222 = -0.150718443 Reorder the terms: -1.022222222 + x = -0.150718443 Solving -1.022222222 + x = -0.150718443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.022222222' to each side of the equation. -1.022222222 + 1.022222222 + x = -0.150718443 + 1.022222222 Combine like terms: -1.022222222 + 1.022222222 = 0.000000000 0.000000000 + x = -0.150718443 + 1.022222222 x = -0.150718443 + 1.022222222 Combine like terms: -0.150718443 + 1.022222222 = 0.871503779 x = 0.871503779 Simplifying x = 0.871503779Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.172940665, 0.871503779}
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