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Simplifying x2 = 16x + -18 Reorder the terms: x2 = -18 + 16x Solving x2 = -18 + 16x Solving for variable 'x'. Reorder the terms: 18 + -16x + x2 = -18 + 16x + 18 + -16x Reorder the terms: 18 + -16x + x2 = -18 + 18 + 16x + -16x Combine like terms: -18 + 18 = 0 18 + -16x + x2 = 0 + 16x + -16x 18 + -16x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 18 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -16x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -16x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -16x + x2 = 0 + -18 -16x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -16x + x2 = -18 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 = -18 + 64 Reorder the terms: 64 + -16x + x2 = -18 + 64 Combine like terms: -18 + 64 = 46 64 + -16x + x2 = 46 Factor a perfect square on the left side: (x + -8)(x + -8) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -8) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -8 = 6.782329983 Simplifying x + -8 = 6.782329983 Reorder the terms: -8 + x = 6.782329983 Solving -8 + x = 6.782329983 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 = 6.782329983 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.782329983 + 8 x = 6.782329983 + 8 Combine like terms: 6.782329983 + 8 = 14.782329983 x = 14.782329983 Simplifying x = 14.782329983Subproblem 2
x + -8 = -6.782329983 Simplifying x + -8 = -6.782329983 Reorder the terms: -8 + x = -6.782329983 Solving -8 + x = -6.782329983 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 = -6.782329983 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.782329983 + 8 x = -6.782329983 + 8 Combine like terms: -6.782329983 + 8 = 1.217670017 x = 1.217670017 Simplifying x = 1.217670017Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.782329983, 1.217670017}
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