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Simplifying (x + -8)(x + -8) = 6 Reorder the terms: (-8 + x)(x + -8) = 6 Reorder the terms: (-8 + x)(-8 + x) = 6 Multiply (-8 + x) * (-8 + x) (-8(-8 + x) + x(-8 + x)) = 6 ((-8 * -8 + x * -8) + x(-8 + x)) = 6 ((64 + -8x) + x(-8 + x)) = 6 (64 + -8x + (-8 * x + x * x)) = 6 (64 + -8x + (-8x + x2)) = 6 Combine like terms: -8x + -8x = -16x (64 + -16x + x2) = 6 Solving 64 + -16x + x2 = 6 Solving for variable 'x'. Reorder the terms: 64 + -6 + -16x + x2 = 6 + -6 Combine like terms: 64 + -6 = 58 58 + -16x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 58 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -16x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -16x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -16x + x2 = 0 + -58 -16x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -16x + x2 = -58 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 = -58 + 64 Reorder the terms: 64 + -16x + x2 = -58 + 64 Combine like terms: -58 + 64 = 6 64 + -16x + x2 = 6 Factor a perfect square on the left side: (x + -8)(x + -8) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -8) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -8 = 2.449489743 Simplifying x + -8 = 2.449489743 Reorder the terms: -8 + x = 2.449489743 Solving -8 + x = 2.449489743 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 = 2.449489743 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.449489743 + 8 x = 2.449489743 + 8 Combine like terms: 2.449489743 + 8 = 10.449489743 x = 10.449489743 Simplifying x = 10.449489743Subproblem 2
x + -8 = -2.449489743 Simplifying x + -8 = -2.449489743 Reorder the terms: -8 + x = -2.449489743 Solving -8 + x = -2.449489743 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 = -2.449489743 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.449489743 + 8 x = -2.449489743 + 8 Combine like terms: -2.449489743 + 8 = 5.550510257 x = 5.550510257 Simplifying x = 5.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.449489743, 5.550510257}
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