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Simplifying x2 = 8x + 336 Reorder the terms: x2 = 336 + 8x Solving x2 = 336 + 8x Solving for variable 'x'. Reorder the terms: -336 + -8x + x2 = 336 + 8x + -336 + -8x Reorder the terms: -336 + -8x + x2 = 336 + -336 + 8x + -8x Combine like terms: 336 + -336 = 0 -336 + -8x + x2 = 0 + 8x + -8x -336 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -336 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + -8x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + -8x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + -8x + x2 = 0 + 336 -8x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 -8x + x2 = 336 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 = 336 + 16 Reorder the terms: 16 + -8x + x2 = 336 + 16 Combine like terms: 336 + 16 = 352 16 + -8x + x2 = 352 Factor a perfect square on the left side: (x + -4)(x + -4) = 352 Calculate the square root of the right side: 18.761663039 Break this problem into two subproblems by setting (x + -4) equal to 18.761663039 and -18.761663039.Subproblem 1
x + -4 = 18.761663039 Simplifying x + -4 = 18.761663039 Reorder the terms: -4 + x = 18.761663039 Solving -4 + x = 18.761663039 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 = 18.761663039 + 4 Combine like terms: -4 + 4 = 0 0 + x = 18.761663039 + 4 x = 18.761663039 + 4 Combine like terms: 18.761663039 + 4 = 22.761663039 x = 22.761663039 Simplifying x = 22.761663039Subproblem 2
x + -4 = -18.761663039 Simplifying x + -4 = -18.761663039 Reorder the terms: -4 + x = -18.761663039 Solving -4 + x = -18.761663039 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 = -18.761663039 + 4 Combine like terms: -4 + 4 = 0 0 + x = -18.761663039 + 4 x = -18.761663039 + 4 Combine like terms: -18.761663039 + 4 = -14.761663039 x = -14.761663039 Simplifying x = -14.761663039Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.761663039, -14.761663039}
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