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Simplifying x2 + -4x + 12 = 6x + -2 Reorder the terms: 12 + -4x + x2 = 6x + -2 Reorder the terms: 12 + -4x + x2 = -2 + 6x Solving 12 + -4x + x2 = -2 + 6x Solving for variable 'x'. Reorder the terms: 12 + 2 + -4x + -6x + x2 = -2 + 6x + 2 + -6x Combine like terms: 12 + 2 = 14 14 + -4x + -6x + x2 = -2 + 6x + 2 + -6x Combine like terms: -4x + -6x = -10x 14 + -10x + x2 = -2 + 6x + 2 + -6x Reorder the terms: 14 + -10x + x2 = -2 + 2 + 6x + -6x Combine like terms: -2 + 2 = 0 14 + -10x + x2 = 0 + 6x + -6x 14 + -10x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 14 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -10x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10x + x2 = 0 + -14 -10x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10x + x2 = -14 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -14 + 25 Reorder the terms: 25 + -10x + x2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10x + x2 = 11 Factor a perfect square on the left side: (x + -5)(x + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -5 = 3.31662479 Simplifying x + -5 = 3.31662479 Reorder the terms: -5 + x = 3.31662479 Solving -5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.31662479 + 5 x = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 x = 8.31662479 Simplifying x = 8.31662479Subproblem 2
x + -5 = -3.31662479 Simplifying x + -5 = -3.31662479 Reorder the terms: -5 + x = -3.31662479 Solving -5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.31662479 + 5 x = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 x = 1.68337521 Simplifying x = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.31662479, 1.68337521}
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