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Simplifying x2 + -4x + -44 = 3x + -6 Reorder the terms: -44 + -4x + x2 = 3x + -6 Reorder the terms: -44 + -4x + x2 = -6 + 3x Solving -44 + -4x + x2 = -6 + 3x Solving for variable 'x'. Reorder the terms: -44 + 6 + -4x + -3x + x2 = -6 + 3x + 6 + -3x Combine like terms: -44 + 6 = -38 -38 + -4x + -3x + x2 = -6 + 3x + 6 + -3x Combine like terms: -4x + -3x = -7x -38 + -7x + x2 = -6 + 3x + 6 + -3x Reorder the terms: -38 + -7x + x2 = -6 + 6 + 3x + -3x Combine like terms: -6 + 6 = 0 -38 + -7x + x2 = 0 + 3x + -3x -38 + -7x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -38 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -7x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -7x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -7x + x2 = 0 + 38 -7x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -7x + x2 = 38 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 38 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 38 + 12.25 Combine like terms: 38 + 12.25 = 50.25 12.25 + -7x + x2 = 50.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -3.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -3.5 = 7.088723439 Simplifying x + -3.5 = 7.088723439 Reorder the terms: -3.5 + x = 7.088723439 Solving -3.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 7.088723439 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.088723439 + 3.5 x = 7.088723439 + 3.5 Combine like terms: 7.088723439 + 3.5 = 10.588723439 x = 10.588723439 Simplifying x = 10.588723439Subproblem 2
x + -3.5 = -7.088723439 Simplifying x + -3.5 = -7.088723439 Reorder the terms: -3.5 + x = -7.088723439 Solving -3.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -7.088723439 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.088723439 + 3.5 x = -7.088723439 + 3.5 Combine like terms: -7.088723439 + 3.5 = -3.588723439 x = -3.588723439 Simplifying x = -3.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.588723439, -3.588723439}
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