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Simplifying x2 + -44x + -96 = 0 Reorder the terms: -96 + -44x + x2 = 0 Solving -96 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -44x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -44x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -44x + x2 = 0 + 96 -44x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -44x + x2 = 96 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = 96 + 484 Reorder the terms: 484 + -44x + x2 = 96 + 484 Combine like terms: 96 + 484 = 580 484 + -44x + x2 = 580 Factor a perfect square on the left side: (x + -22)(x + -22) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (x + -22) equal to 24.083189158 and -24.083189158.Subproblem 1
x + -22 = 24.083189158 Simplifying x + -22 = 24.083189158 Reorder the terms: -22 + x = 24.083189158 Solving -22 + x = 24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 24.083189158 + 22 Combine like terms: -22 + 22 = 0 0 + x = 24.083189158 + 22 x = 24.083189158 + 22 Combine like terms: 24.083189158 + 22 = 46.083189158 x = 46.083189158 Simplifying x = 46.083189158Subproblem 2
x + -22 = -24.083189158 Simplifying x + -22 = -24.083189158 Reorder the terms: -22 + x = -24.083189158 Solving -22 + x = -24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -24.083189158 + 22 Combine like terms: -22 + 22 = 0 0 + x = -24.083189158 + 22 x = -24.083189158 + 22 Combine like terms: -24.083189158 + 22 = -2.083189158 x = -2.083189158 Simplifying x = -2.083189158Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.083189158, -2.083189158}
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