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Simplifying 0.024x2 + -1x = 5.5 Reorder the terms: -1x + 0.024x2 = 5.5 Solving -1x + 0.024x2 = 5.5 Solving for variable 'x'. Reorder the terms: -5.5 + -1x + 0.024x2 = 5.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 -5.5 + -1x + 0.024x2 = 0.0 Begin completing the square. Divide all terms by 0.024 the coefficient of the squared term: Divide each side by '0.024'. -229.1666667 + -41.66666667x + x2 = 0 Move the constant term to the right: Add '229.1666667' to each side of the equation. -229.1666667 + -41.66666667x + 229.1666667 + x2 = 0 + 229.1666667 Reorder the terms: -229.1666667 + 229.1666667 + -41.66666667x + x2 = 0 + 229.1666667 Combine like terms: -229.1666667 + 229.1666667 = 0.0000000 0.0000000 + -41.66666667x + x2 = 0 + 229.1666667 -41.66666667x + x2 = 0 + 229.1666667 Combine like terms: 0 + 229.1666667 = 229.1666667 -41.66666667x + x2 = 229.1666667 The x term is -41.66666667x. Take half its coefficient (-20.83333334). Square it (434.0277781) and add it to both sides. Add '434.0277781' to each side of the equation. -41.66666667x + 434.0277781 + x2 = 229.1666667 + 434.0277781 Reorder the terms: 434.0277781 + -41.66666667x + x2 = 229.1666667 + 434.0277781 Combine like terms: 229.1666667 + 434.0277781 = 663.1944448 434.0277781 + -41.66666667x + x2 = 663.1944448 Factor a perfect square on the left side: (x + -20.83333334)(x + -20.83333334) = 663.1944448 Calculate the square root of the right side: 25.752561908 Break this problem into two subproblems by setting (x + -20.83333334) equal to 25.752561908 and -25.752561908.Subproblem 1
x + -20.83333334 = 25.752561908 Simplifying x + -20.83333334 = 25.752561908 Reorder the terms: -20.83333334 + x = 25.752561908 Solving -20.83333334 + x = 25.752561908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.83333334' to each side of the equation. -20.83333334 + 20.83333334 + x = 25.752561908 + 20.83333334 Combine like terms: -20.83333334 + 20.83333334 = 0.00000000 0.00000000 + x = 25.752561908 + 20.83333334 x = 25.752561908 + 20.83333334 Combine like terms: 25.752561908 + 20.83333334 = 46.585895248 x = 46.585895248 Simplifying x = 46.585895248Subproblem 2
x + -20.83333334 = -25.752561908 Simplifying x + -20.83333334 = -25.752561908 Reorder the terms: -20.83333334 + x = -25.752561908 Solving -20.83333334 + x = -25.752561908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.83333334' to each side of the equation. -20.83333334 + 20.83333334 + x = -25.752561908 + 20.83333334 Combine like terms: -20.83333334 + 20.83333334 = 0.00000000 0.00000000 + x = -25.752561908 + 20.83333334 x = -25.752561908 + 20.83333334 Combine like terms: -25.752561908 + 20.83333334 = -4.919228568 x = -4.919228568 Simplifying x = -4.919228568Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.585895248, -4.919228568}
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