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Simplifying (x + -16)(x + -16) = 18 Reorder the terms: (-16 + x)(x + -16) = 18 Reorder the terms: (-16 + x)(-16 + x) = 18 Multiply (-16 + x) * (-16 + x) (-16(-16 + x) + x(-16 + x)) = 18 ((-16 * -16 + x * -16) + x(-16 + x)) = 18 ((256 + -16x) + x(-16 + x)) = 18 (256 + -16x + (-16 * x + x * x)) = 18 (256 + -16x + (-16x + x2)) = 18 Combine like terms: -16x + -16x = -32x (256 + -32x + x2) = 18 Solving 256 + -32x + x2 = 18 Solving for variable 'x'. Reorder the terms: 256 + -18 + -32x + x2 = 18 + -18 Combine like terms: 256 + -18 = 238 238 + -32x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 238 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-238' to each side of the equation. 238 + -32x + -238 + x2 = 0 + -238 Reorder the terms: 238 + -238 + -32x + x2 = 0 + -238 Combine like terms: 238 + -238 = 0 0 + -32x + x2 = 0 + -238 -32x + x2 = 0 + -238 Combine like terms: 0 + -238 = -238 -32x + x2 = -238 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -238 + 256 Reorder the terms: 256 + -32x + x2 = -238 + 256 Combine like terms: -238 + 256 = 18 256 + -32x + x2 = 18 Factor a perfect square on the left side: (x + -16)(x + -16) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -16) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -16 = 4.242640687 Simplifying x + -16 = 4.242640687 Reorder the terms: -16 + x = 4.242640687 Solving -16 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 4.242640687 + 16 Combine like terms: -16 + 16 = 0 0 + x = 4.242640687 + 16 x = 4.242640687 + 16 Combine like terms: 4.242640687 + 16 = 20.242640687 x = 20.242640687 Simplifying x = 20.242640687Subproblem 2
x + -16 = -4.242640687 Simplifying x + -16 = -4.242640687 Reorder the terms: -16 + x = -4.242640687 Solving -16 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -4.242640687 + 16 Combine like terms: -16 + 16 = 0 0 + x = -4.242640687 + 16 x = -4.242640687 + 16 Combine like terms: -4.242640687 + 16 = 11.757359313 x = 11.757359313 Simplifying x = 11.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.242640687, 11.757359313}
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