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Simplifying -16x2 + 128x + 389 = 0 Reorder the terms: 389 + 128x + -16x2 = 0 Solving 389 + 128x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -24.3125 + -8x + x2 = 0 Move the constant term to the right: Add '24.3125' to each side of the equation. -24.3125 + -8x + 24.3125 + x2 = 0 + 24.3125 Reorder the terms: -24.3125 + 24.3125 + -8x + x2 = 0 + 24.3125 Combine like terms: -24.3125 + 24.3125 = 0.0000 0.0000 + -8x + x2 = 0 + 24.3125 -8x + x2 = 0 + 24.3125 Combine like terms: 0 + 24.3125 = 24.3125 -8x + x2 = 24.3125 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 = 24.3125 + 16 Reorder the terms: 16 + -8x + x2 = 24.3125 + 16 Combine like terms: 24.3125 + 16 = 40.3125 16 + -8x + x2 = 40.3125 Factor a perfect square on the left side: (x + -4)(x + -4) = 40.3125 Calculate the square root of the right side: 6.34921255 Break this problem into two subproblems by setting (x + -4) equal to 6.34921255 and -6.34921255.Subproblem 1
x + -4 = 6.34921255 Simplifying x + -4 = 6.34921255 Reorder the terms: -4 + x = 6.34921255 Solving -4 + x = 6.34921255 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 = 6.34921255 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.34921255 + 4 x = 6.34921255 + 4 Combine like terms: 6.34921255 + 4 = 10.34921255 x = 10.34921255 Simplifying x = 10.34921255Subproblem 2
x + -4 = -6.34921255 Simplifying x + -4 = -6.34921255 Reorder the terms: -4 + x = -6.34921255 Solving -4 + x = -6.34921255 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 = -6.34921255 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.34921255 + 4 x = -6.34921255 + 4 Combine like terms: -6.34921255 + 4 = -2.34921255 x = -2.34921255 Simplifying x = -2.34921255Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.34921255, -2.34921255}
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