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Simplifying x^{2}+ 16x = -7 Reorder the terms: 16x + x^{2}= -7 Solving 16x + x^{2}= -7 Solving for variable 'x'. Reorder the terms: 7 + 16x + x^{2}= -7 + 7 Combine like terms: -7 + 7 = 0 7 + 16x + x^{2}= 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 16x + -7 + x^{2}= 0 + -7 Reorder the terms: 7 + -7 + 16x + x^{2}= 0 + -7 Combine like terms: 7 + -7 = 0 0 + 16x + x^{2}= 0 + -7 16x + x^{2}= 0 + -7 Combine like terms: 0 + -7 = -7 16x + x^{2}= -7 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 + x^{2}= -7 + 64 Reorder the terms: 64 + 16x + x^{2}= -7 + 64 Combine like terms: -7 + 64 = 57 64 + 16x + x^{2}= 57 Factor a perfect square on the left side: (x + 8)(x + 8) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 8) equal to 7.549834435 and -7.549834435.## Subproblem 1

x + 8 = 7.549834435 Simplifying x + 8 = 7.549834435 Reorder the terms: 8 + x = 7.549834435 Solving 8 + x = 7.549834435 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 = 7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.549834435 + -8 x = 7.549834435 + -8 Combine like terms: 7.549834435 + -8 = -0.450165565 x = -0.450165565 Simplifying x = -0.450165565## Subproblem 2

x + 8 = -7.549834435 Simplifying x + 8 = -7.549834435 Reorder the terms: 8 + x = -7.549834435 Solving 8 + x = -7.549834435 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 = -7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.549834435 + -8 x = -7.549834435 + -8 Combine like terms: -7.549834435 + -8 = -15.549834435 x = -15.549834435 Simplifying x = -15.549834435## Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.450165565, -15.549834435}

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