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Simplifying x2 = -16x + -32 Reorder the terms: x2 = -32 + -16x Solving x2 = -32 + -16x Solving for variable 'x'. Reorder the terms: 32 + 16x + x2 = -32 + -16x + 32 + 16x Reorder the terms: 32 + 16x + x2 = -32 + 32 + -16x + 16x Combine like terms: -32 + 32 = 0 32 + 16x + x2 = 0 + -16x + 16x 32 + 16x + x2 = -16x + 16x Combine like terms: -16x + 16x = 0 32 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 16x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 16x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 16x + x2 = 0 + -32 16x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 16x + x2 = -32 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 = -32 + 64 Reorder the terms: 64 + 16x + x2 = -32 + 64 Combine like terms: -32 + 64 = 32 64 + 16x + x2 = 32 Factor a perfect square on the left side: (x + 8)(x + 8) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 8) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 8 = 5.656854249 Simplifying x + 8 = 5.656854249 Reorder the terms: 8 + x = 5.656854249 Solving 8 + x = 5.656854249 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 = 5.656854249 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.656854249 + -8 x = 5.656854249 + -8 Combine like terms: 5.656854249 + -8 = -2.343145751 x = -2.343145751 Simplifying x = -2.343145751Subproblem 2
x + 8 = -5.656854249 Simplifying x + 8 = -5.656854249 Reorder the terms: 8 + x = -5.656854249 Solving 8 + x = -5.656854249 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 = -5.656854249 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.656854249 + -8 x = -5.656854249 + -8 Combine like terms: -5.656854249 + -8 = -13.656854249 x = -13.656854249 Simplifying x = -13.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.343145751, -13.656854249}
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