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Simplifying (x + 8)(x + 8) = 12 Reorder the terms: (8 + x)(x + 8) = 12 Reorder the terms: (8 + x)(8 + x) = 12 Multiply (8 + x) * (8 + x) (8(8 + x) + x(8 + x)) = 12 ((8 * 8 + x * 8) + x(8 + x)) = 12 ((64 + 8x) + x(8 + x)) = 12 (64 + 8x + (8 * x + x * x)) = 12 (64 + 8x + (8x + x2)) = 12 Combine like terms: 8x + 8x = 16x (64 + 16x + x2) = 12 Solving 64 + 16x + x2 = 12 Solving for variable 'x'. Reorder the terms: 64 + -12 + 16x + x2 = 12 + -12 Combine like terms: 64 + -12 = 52 52 + 16x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 52 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 16x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + 16x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 16x + x2 = 0 + -52 16x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 16x + x2 = -52 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -52 + 64 Reorder the terms: 64 + 16x + x2 = -52 + 64 Combine like terms: -52 + 64 = 12 64 + 16x + x2 = 12 Factor a perfect square on the left side: (x + 8)(x + 8) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 8) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 8 = 3.464101615 Simplifying x + 8 = 3.464101615 Reorder the terms: 8 + x = 3.464101615 Solving 8 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 3.464101615 + -8 Combine like terms: 8 + -8 = 0 0 + x = 3.464101615 + -8 x = 3.464101615 + -8 Combine like terms: 3.464101615 + -8 = -4.535898385 x = -4.535898385 Simplifying x = -4.535898385Subproblem 2
x + 8 = -3.464101615 Simplifying x + 8 = -3.464101615 Reorder the terms: 8 + x = -3.464101615 Solving 8 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -3.464101615 + -8 Combine like terms: 8 + -8 = 0 0 + x = -3.464101615 + -8 x = -3.464101615 + -8 Combine like terms: -3.464101615 + -8 = -11.464101615 x = -11.464101615 Simplifying x = -11.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.535898385, -11.464101615}
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