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Simplifying x2 + -72x + 256 = 0 Reorder the terms: 256 + -72x + x2 = 0 Solving 256 + -72x + 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 + -72x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + -72x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -72x + x2 = 0 + -256 -72x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 -72x + x2 = -256 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = -256 + 1296 Reorder the terms: 1296 + -72x + x2 = -256 + 1296 Combine like terms: -256 + 1296 = 1040 1296 + -72x + x2 = 1040 Factor a perfect square on the left side: (x + -36)(x + -36) = 1040 Calculate the square root of the right side: 32.249030993 Break this problem into two subproblems by setting (x + -36) equal to 32.249030993 and -32.249030993.Subproblem 1
x + -36 = 32.249030993 Simplifying x + -36 = 32.249030993 Reorder the terms: -36 + x = 32.249030993 Solving -36 + x = 32.249030993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 32.249030993 + 36 Combine like terms: -36 + 36 = 0 0 + x = 32.249030993 + 36 x = 32.249030993 + 36 Combine like terms: 32.249030993 + 36 = 68.249030993 x = 68.249030993 Simplifying x = 68.249030993Subproblem 2
x + -36 = -32.249030993 Simplifying x + -36 = -32.249030993 Reorder the terms: -36 + x = -32.249030993 Solving -36 + x = -32.249030993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -32.249030993 + 36 Combine like terms: -36 + 36 = 0 0 + x = -32.249030993 + 36 x = -32.249030993 + 36 Combine like terms: -32.249030993 + 36 = 3.750969007 x = 3.750969007 Simplifying x = 3.750969007Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.249030993, 3.750969007}
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