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Simplifying x2 + 8x = 50 Reorder the terms: 8x + x2 = 50 Solving 8x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 8x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 8x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 8x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 8x + x2 = 0 + 50 8x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 8x + x2 = 50 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 = 50 + 16 Reorder the terms: 16 + 8x + x2 = 50 + 16 Combine like terms: 50 + 16 = 66 16 + 8x + x2 = 66 Factor a perfect square on the left side: (x + 4)(x + 4) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 4) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 4 = 8.124038405 Simplifying x + 4 = 8.124038405 Reorder the terms: 4 + x = 8.124038405 Solving 4 + x = 8.124038405 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 = 8.124038405 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.124038405 + -4 x = 8.124038405 + -4 Combine like terms: 8.124038405 + -4 = 4.124038405 x = 4.124038405 Simplifying x = 4.124038405Subproblem 2
x + 4 = -8.124038405 Simplifying x + 4 = -8.124038405 Reorder the terms: 4 + x = -8.124038405 Solving 4 + x = -8.124038405 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 = -8.124038405 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.124038405 + -4 x = -8.124038405 + -4 Combine like terms: -8.124038405 + -4 = -12.124038405 x = -12.124038405 Simplifying x = -12.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.124038405, -12.124038405}
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