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Simplifying x2 + 8x + -2 = 49 Reorder the terms: -2 + 8x + x2 = 49 Solving -2 + 8x + x2 = 49 Solving for variable 'x'. Reorder the terms: -2 + -49 + 8x + x2 = 49 + -49 Combine like terms: -2 + -49 = -51 -51 + 8x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -51 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 8x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 8x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 8x + x2 = 0 + 51 8x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 8x + x2 = 51 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 = 51 + 16 Reorder the terms: 16 + 8x + x2 = 51 + 16 Combine like terms: 51 + 16 = 67 16 + 8x + x2 = 67 Factor a perfect square on the left side: (x + 4)(x + 4) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 4) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 4 = 8.185352772 Simplifying x + 4 = 8.185352772 Reorder the terms: 4 + x = 8.185352772 Solving 4 + x = 8.185352772 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 = 8.185352772 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.185352772 + -4 x = 8.185352772 + -4 Combine like terms: 8.185352772 + -4 = 4.185352772 x = 4.185352772 Simplifying x = 4.185352772Subproblem 2
x + 4 = -8.185352772 Simplifying x + 4 = -8.185352772 Reorder the terms: 4 + x = -8.185352772 Solving 4 + x = -8.185352772 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 = -8.185352772 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.185352772 + -4 x = -8.185352772 + -4 Combine like terms: -8.185352772 + -4 = -12.185352772 x = -12.185352772 Simplifying x = -12.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.185352772, -12.185352772}
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