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Simplifying x2 + 6x + -256 = 0 Reorder the terms: -256 + 6x + x2 = 0 Solving -256 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 6x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 6x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 6x + x2 = 0 + 256 6x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 6x + x2 = 256 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 256 + 9 Reorder the terms: 9 + 6x + x2 = 256 + 9 Combine like terms: 256 + 9 = 265 9 + 6x + x2 = 265 Factor a perfect square on the left side: (x + 3)(x + 3) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (x + 3) equal to 16.278820596 and -16.278820596.Subproblem 1
x + 3 = 16.278820596 Simplifying x + 3 = 16.278820596 Reorder the terms: 3 + x = 16.278820596 Solving 3 + x = 16.278820596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 16.278820596 + -3 Combine like terms: 3 + -3 = 0 0 + x = 16.278820596 + -3 x = 16.278820596 + -3 Combine like terms: 16.278820596 + -3 = 13.278820596 x = 13.278820596 Simplifying x = 13.278820596Subproblem 2
x + 3 = -16.278820596 Simplifying x + 3 = -16.278820596 Reorder the terms: 3 + x = -16.278820596 Solving 3 + x = -16.278820596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -16.278820596 + -3 Combine like terms: 3 + -3 = 0 0 + x = -16.278820596 + -3 x = -16.278820596 + -3 Combine like terms: -16.278820596 + -3 = -19.278820596 x = -19.278820596 Simplifying x = -19.278820596Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.278820596, -19.278820596}
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