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Simplifying x2 + -16x + -540 = 0 Reorder the terms: -540 + -16x + x2 = 0 Solving -540 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + -16x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + -16x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + -16x + x2 = 0 + 540 -16x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 -16x + x2 = 540 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 540 + 64 Reorder the terms: 64 + -16x + x2 = 540 + 64 Combine like terms: 540 + 64 = 604 64 + -16x + x2 = 604 Factor a perfect square on the left side: (x + -8)(x + -8) = 604 Calculate the square root of the right side: 24.576411455 Break this problem into two subproblems by setting (x + -8) equal to 24.576411455 and -24.576411455.Subproblem 1
x + -8 = 24.576411455 Simplifying x + -8 = 24.576411455 Reorder the terms: -8 + x = 24.576411455 Solving -8 + x = 24.576411455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 24.576411455 + 8 Combine like terms: -8 + 8 = 0 0 + x = 24.576411455 + 8 x = 24.576411455 + 8 Combine like terms: 24.576411455 + 8 = 32.576411455 x = 32.576411455 Simplifying x = 32.576411455Subproblem 2
x + -8 = -24.576411455 Simplifying x + -8 = -24.576411455 Reorder the terms: -8 + x = -24.576411455 Solving -8 + x = -24.576411455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -24.576411455 + 8 Combine like terms: -8 + 8 = 0 0 + x = -24.576411455 + 8 x = -24.576411455 + 8 Combine like terms: -24.576411455 + 8 = -16.576411455 x = -16.576411455 Simplifying x = -16.576411455Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.576411455, -16.576411455}
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