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Simplifying x2 + -8x + -192 = 0 Reorder the terms: -192 + -8x + x2 = 0 Solving -192 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + -8x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + -8x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -8x + x2 = 0 + 192 -8x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 -8x + x2 = 192 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 = 192 + 16 Reorder the terms: 16 + -8x + x2 = 192 + 16 Combine like terms: 192 + 16 = 208 16 + -8x + x2 = 208 Factor a perfect square on the left side: (x + -4)(x + -4) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + -4) equal to 14.422205102 and -14.422205102.Subproblem 1
x + -4 = 14.422205102 Simplifying x + -4 = 14.422205102 Reorder the terms: -4 + x = 14.422205102 Solving -4 + x = 14.422205102 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 = 14.422205102 + 4 Combine like terms: -4 + 4 = 0 0 + x = 14.422205102 + 4 x = 14.422205102 + 4 Combine like terms: 14.422205102 + 4 = 18.422205102 x = 18.422205102 Simplifying x = 18.422205102Subproblem 2
x + -4 = -14.422205102 Simplifying x + -4 = -14.422205102 Reorder the terms: -4 + x = -14.422205102 Solving -4 + x = -14.422205102 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 = -14.422205102 + 4 Combine like terms: -4 + 4 = 0 0 + x = -14.422205102 + 4 x = -14.422205102 + 4 Combine like terms: -14.422205102 + 4 = -10.422205102 x = -10.422205102 Simplifying x = -10.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.422205102, -10.422205102}
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