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Simplifying x2 + 6 = -8x + 12 Reorder the terms: 6 + x2 = -8x + 12 Reorder the terms: 6 + x2 = 12 + -8x Solving 6 + x2 = 12 + -8x Solving for variable 'x'. Reorder the terms: 6 + -12 + 8x + x2 = 12 + -8x + -12 + 8x Combine like terms: 6 + -12 = -6 -6 + 8x + x2 = 12 + -8x + -12 + 8x Reorder the terms: -6 + 8x + x2 = 12 + -12 + -8x + 8x Combine like terms: 12 + -12 = 0 -6 + 8x + x2 = 0 + -8x + 8x -6 + 8x + x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -6 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 8x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 8x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 8x + x2 = 0 + 6 8x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 8x + x2 = 6 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 6 + 16 Reorder the terms: 16 + 8x + x2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + 8x + x2 = 22 Factor a perfect square on the left side: (x + 4)(x + 4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 4) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 4 = 4.69041576 Simplifying x + 4 = 4.69041576 Reorder the terms: 4 + x = 4.69041576 Solving 4 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.69041576 + -4 x = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 x = 0.69041576 Simplifying x = 0.69041576Subproblem 2
x + 4 = -4.69041576 Simplifying x + 4 = -4.69041576 Reorder the terms: 4 + x = -4.69041576 Solving 4 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.69041576 + -4 x = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 x = -8.69041576 Simplifying x = -8.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.69041576, -8.69041576}
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