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Simplifying x2 + -8x = 242 Reorder the terms: -8x + x2 = 242 Solving -8x + x2 = 242 Solving for variable 'x'. Reorder the terms: -242 + -8x + x2 = 242 + -242 Combine like terms: 242 + -242 = 0 -242 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '242' to each side of the equation. -242 + -8x + 242 + x2 = 0 + 242 Reorder the terms: -242 + 242 + -8x + x2 = 0 + 242 Combine like terms: -242 + 242 = 0 0 + -8x + x2 = 0 + 242 -8x + x2 = 0 + 242 Combine like terms: 0 + 242 = 242 -8x + x2 = 242 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 = 242 + 16 Reorder the terms: 16 + -8x + x2 = 242 + 16 Combine like terms: 242 + 16 = 258 16 + -8x + x2 = 258 Factor a perfect square on the left side: (x + -4)(x + -4) = 258 Calculate the square root of the right side: 16.062378404 Break this problem into two subproblems by setting (x + -4) equal to 16.062378404 and -16.062378404.Subproblem 1
x + -4 = 16.062378404 Simplifying x + -4 = 16.062378404 Reorder the terms: -4 + x = 16.062378404 Solving -4 + x = 16.062378404 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 = 16.062378404 + 4 Combine like terms: -4 + 4 = 0 0 + x = 16.062378404 + 4 x = 16.062378404 + 4 Combine like terms: 16.062378404 + 4 = 20.062378404 x = 20.062378404 Simplifying x = 20.062378404Subproblem 2
x + -4 = -16.062378404 Simplifying x + -4 = -16.062378404 Reorder the terms: -4 + x = -16.062378404 Solving -4 + x = -16.062378404 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 = -16.062378404 + 4 Combine like terms: -4 + 4 = 0 0 + x = -16.062378404 + 4 x = -16.062378404 + 4 Combine like terms: -16.062378404 + 4 = -12.062378404 x = -12.062378404 Simplifying x = -12.062378404Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.062378404, -12.062378404}
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