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Simplifying 11x(4x + -9) = 23 Reorder the terms: 11x(-9 + 4x) = 23 (-9 * 11x + 4x * 11x) = 23 (-99x + 44x2) = 23 Solving -99x + 44x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -99x + 44x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -99x + 44x2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.5227272727 + -2.25x + x2 = 0 Move the constant term to the right: Add '0.5227272727' to each side of the equation. -0.5227272727 + -2.25x + 0.5227272727 + x2 = 0 + 0.5227272727 Reorder the terms: -0.5227272727 + 0.5227272727 + -2.25x + x2 = 0 + 0.5227272727 Combine like terms: -0.5227272727 + 0.5227272727 = 0.0000000000 0.0000000000 + -2.25x + x2 = 0 + 0.5227272727 -2.25x + x2 = 0 + 0.5227272727 Combine like terms: 0 + 0.5227272727 = 0.5227272727 -2.25x + x2 = 0.5227272727 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 0.5227272727 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 0.5227272727 + 1.265625 Combine like terms: 0.5227272727 + 1.265625 = 1.7883522727 1.265625 + -2.25x + x2 = 1.7883522727 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 1.7883522727 Calculate the square root of the right side: 1.33729289 Break this problem into two subproblems by setting (x + -1.125) equal to 1.33729289 and -1.33729289.Subproblem 1
x + -1.125 = 1.33729289 Simplifying x + -1.125 = 1.33729289 Reorder the terms: -1.125 + x = 1.33729289 Solving -1.125 + x = 1.33729289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.33729289 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.33729289 + 1.125 x = 1.33729289 + 1.125 Combine like terms: 1.33729289 + 1.125 = 2.46229289 x = 2.46229289 Simplifying x = 2.46229289Subproblem 2
x + -1.125 = -1.33729289 Simplifying x + -1.125 = -1.33729289 Reorder the terms: -1.125 + x = -1.33729289 Solving -1.125 + x = -1.33729289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.33729289 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.33729289 + 1.125 x = -1.33729289 + 1.125 Combine like terms: -1.33729289 + 1.125 = -0.21229289 x = -0.21229289 Simplifying x = -0.21229289Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.46229289, -0.21229289}
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