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Simplifying x2 + -6x + -27 = -2x + -5 Reorder the terms: -27 + -6x + x2 = -2x + -5 Reorder the terms: -27 + -6x + x2 = -5 + -2x Solving -27 + -6x + x2 = -5 + -2x Solving for variable 'x'. Reorder the terms: -27 + 5 + -6x + 2x + x2 = -5 + -2x + 5 + 2x Combine like terms: -27 + 5 = -22 -22 + -6x + 2x + x2 = -5 + -2x + 5 + 2x Combine like terms: -6x + 2x = -4x -22 + -4x + x2 = -5 + -2x + 5 + 2x Reorder the terms: -22 + -4x + x2 = -5 + 5 + -2x + 2x Combine like terms: -5 + 5 = 0 -22 + -4x + x2 = 0 + -2x + 2x -22 + -4x + x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -22 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -4x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -4x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -4x + x2 = 0 + 22 -4x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -4x + x2 = 22 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 22 + 4 Reorder the terms: 4 + -4x + x2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + -4x + x2 = 26 Factor a perfect square on the left side: (x + -2)(x + -2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -2) equal to 5.099019514 and -5.099019514.Subproblem 1
x + -2 = 5.099019514 Simplifying x + -2 = 5.099019514 Reorder the terms: -2 + x = 5.099019514 Solving -2 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.099019514 + 2 x = 5.099019514 + 2 Combine like terms: 5.099019514 + 2 = 7.099019514 x = 7.099019514 Simplifying x = 7.099019514Subproblem 2
x + -2 = -5.099019514 Simplifying x + -2 = -5.099019514 Reorder the terms: -2 + x = -5.099019514 Solving -2 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.099019514 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.099019514 + 2 x = -5.099019514 + 2 Combine like terms: -5.099019514 + 2 = -3.099019514 x = -3.099019514 Simplifying x = -3.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.099019514, -3.099019514}
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