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Simplifying x2 + 16x = -16 Reorder the terms: 16x + x2 = -16 Solving 16x + x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 16x + x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 16x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 16x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 16x + x2 = 0 + -16 16x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 16x + x2 = -16 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 = -16 + 64 Reorder the terms: 64 + 16x + x2 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + 16x + x2 = 48 Factor a perfect square on the left side: (x + 8)(x + 8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 8) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 8 = 6.92820323 Simplifying x + 8 = 6.92820323 Reorder the terms: 8 + x = 6.92820323 Solving 8 + x = 6.92820323 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 = 6.92820323 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.92820323 + -8 x = 6.92820323 + -8 Combine like terms: 6.92820323 + -8 = -1.07179677 x = -1.07179677 Simplifying x = -1.07179677Subproblem 2
x + 8 = -6.92820323 Simplifying x + 8 = -6.92820323 Reorder the terms: 8 + x = -6.92820323 Solving 8 + x = -6.92820323 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 = -6.92820323 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.92820323 + -8 x = -6.92820323 + -8 Combine like terms: -6.92820323 + -8 = -14.92820323 x = -14.92820323 Simplifying x = -14.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.07179677, -14.92820323}
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