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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 = 10.422205102 x = 10.422205102 Simplifying x = 10.422205102Subproblem 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 = -18.422205102 x = -18.422205102 Simplifying x = -18.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.422205102, -18.422205102}
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