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Simplifying x2 + 6x = 255 Reorder the terms: 6x + x2 = 255 Solving 6x + x2 = 255 Solving for variable 'x'. Reorder the terms: -255 + 6x + x2 = 255 + -255 Combine like terms: 255 + -255 = 0 -255 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + 6x + 255 + x2 = 0 + 255 Reorder the terms: -255 + 255 + 6x + x2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + 6x + x2 = 0 + 255 6x + x2 = 0 + 255 Combine like terms: 0 + 255 = 255 6x + x2 = 255 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 = 255 + 9 Reorder the terms: 9 + 6x + x2 = 255 + 9 Combine like terms: 255 + 9 = 264 9 + 6x + x2 = 264 Factor a perfect square on the left side: (x + 3)(x + 3) = 264 Calculate the square root of the right side: 16.248076809 Break this problem into two subproblems by setting (x + 3) equal to 16.248076809 and -16.248076809.Subproblem 1
x + 3 = 16.248076809 Simplifying x + 3 = 16.248076809 Reorder the terms: 3 + x = 16.248076809 Solving 3 + x = 16.248076809 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 = 16.248076809 + -3 Combine like terms: 3 + -3 = 0 0 + x = 16.248076809 + -3 x = 16.248076809 + -3 Combine like terms: 16.248076809 + -3 = 13.248076809 x = 13.248076809 Simplifying x = 13.248076809Subproblem 2
x + 3 = -16.248076809 Simplifying x + 3 = -16.248076809 Reorder the terms: 3 + x = -16.248076809 Solving 3 + x = -16.248076809 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 = -16.248076809 + -3 Combine like terms: 3 + -3 = 0 0 + x = -16.248076809 + -3 x = -16.248076809 + -3 Combine like terms: -16.248076809 + -3 = -19.248076809 x = -19.248076809 Simplifying x = -19.248076809Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.248076809, -19.248076809}
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