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Simplifying 33x2 + -555x + 1111 = 0 Reorder the terms: 1111 + -555x + 33x2 = 0 Solving 1111 + -555x + 33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. 33.66666667 + -16.81818182x + x2 = 0 Move the constant term to the right: Add '-33.66666667' to each side of the equation. 33.66666667 + -16.81818182x + -33.66666667 + x2 = 0 + -33.66666667 Reorder the terms: 33.66666667 + -33.66666667 + -16.81818182x + x2 = 0 + -33.66666667 Combine like terms: 33.66666667 + -33.66666667 = 0.00000000 0.00000000 + -16.81818182x + x2 = 0 + -33.66666667 -16.81818182x + x2 = 0 + -33.66666667 Combine like terms: 0 + -33.66666667 = -33.66666667 -16.81818182x + x2 = -33.66666667 The x term is -16.81818182x. Take half its coefficient (-8.40909091). Square it (70.71280993) and add it to both sides. Add '70.71280993' to each side of the equation. -16.81818182x + 70.71280993 + x2 = -33.66666667 + 70.71280993 Reorder the terms: 70.71280993 + -16.81818182x + x2 = -33.66666667 + 70.71280993 Combine like terms: -33.66666667 + 70.71280993 = 37.04614326 70.71280993 + -16.81818182x + x2 = 37.04614326 Factor a perfect square on the left side: (x + -8.40909091)(x + -8.40909091) = 37.04614326 Calculate the square root of the right side: 6.086554301 Break this problem into two subproblems by setting (x + -8.40909091) equal to 6.086554301 and -6.086554301.Subproblem 1
x + -8.40909091 = 6.086554301 Simplifying x + -8.40909091 = 6.086554301 Reorder the terms: -8.40909091 + x = 6.086554301 Solving -8.40909091 + x = 6.086554301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.40909091' to each side of the equation. -8.40909091 + 8.40909091 + x = 6.086554301 + 8.40909091 Combine like terms: -8.40909091 + 8.40909091 = 0.00000000 0.00000000 + x = 6.086554301 + 8.40909091 x = 6.086554301 + 8.40909091 Combine like terms: 6.086554301 + 8.40909091 = 14.495645211 x = 14.495645211 Simplifying x = 14.495645211Subproblem 2
x + -8.40909091 = -6.086554301 Simplifying x + -8.40909091 = -6.086554301 Reorder the terms: -8.40909091 + x = -6.086554301 Solving -8.40909091 + x = -6.086554301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.40909091' to each side of the equation. -8.40909091 + 8.40909091 + x = -6.086554301 + 8.40909091 Combine like terms: -8.40909091 + 8.40909091 = 0.00000000 0.00000000 + x = -6.086554301 + 8.40909091 x = -6.086554301 + 8.40909091 Combine like terms: -6.086554301 + 8.40909091 = 2.322536609 x = 2.322536609 Simplifying x = 2.322536609Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.495645211, 2.322536609}
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