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Simplifying 4x2 + -33x + 18 = 0 Reorder the terms: 18 + -33x + 4x2 = 0 Solving 18 + -33x + 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'. 4.5 + -8.25x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -8.25x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -8.25x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -8.25x + x2 = 0 + -4.5 -8.25x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -8.25x + x2 = -4.5 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = -4.5 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -4.5 + 17.015625 Combine like terms: -4.5 + 17.015625 = 12.515625 17.015625 + -8.25x + x2 = 12.515625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 12.515625 Calculate the square root of the right side: 3.537742925 Break this problem into two subproblems by setting (x + -4.125) equal to 3.537742925 and -3.537742925.Subproblem 1
x + -4.125 = 3.537742925 Simplifying x + -4.125 = 3.537742925 Reorder the terms: -4.125 + x = 3.537742925 Solving -4.125 + x = 3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 3.537742925 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 3.537742925 + 4.125 x = 3.537742925 + 4.125 Combine like terms: 3.537742925 + 4.125 = 7.662742925 x = 7.662742925 Simplifying x = 7.662742925Subproblem 2
x + -4.125 = -3.537742925 Simplifying x + -4.125 = -3.537742925 Reorder the terms: -4.125 + x = -3.537742925 Solving -4.125 + x = -3.537742925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -3.537742925 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -3.537742925 + 4.125 x = -3.537742925 + 4.125 Combine like terms: -3.537742925 + 4.125 = 0.587257075 x = 0.587257075 Simplifying x = 0.587257075Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.662742925, 0.587257075}
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