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Simplifying x2 + -512x + 36 = 0 Reorder the terms: 36 + -512x + x2 = 0 Solving 36 + -512x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -512x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -512x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -512x + x2 = 0 + -36 -512x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -512x + x2 = -36 The x term is -512x. Take half its coefficient (-256). Square it (65536) and add it to both sides. Add '65536' to each side of the equation. -512x + 65536 + x2 = -36 + 65536 Reorder the terms: 65536 + -512x + x2 = -36 + 65536 Combine like terms: -36 + 65536 = 65500 65536 + -512x + x2 = 65500 Factor a perfect square on the left side: (x + -256)(x + -256) = 65500 Calculate the square root of the right side: 255.929677841 Break this problem into two subproblems by setting (x + -256) equal to 255.929677841 and -255.929677841.Subproblem 1
x + -256 = 255.929677841 Simplifying x + -256 = 255.929677841 Reorder the terms: -256 + x = 255.929677841 Solving -256 + x = 255.929677841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '256' to each side of the equation. -256 + 256 + x = 255.929677841 + 256 Combine like terms: -256 + 256 = 0 0 + x = 255.929677841 + 256 x = 255.929677841 + 256 Combine like terms: 255.929677841 + 256 = 511.929677841 x = 511.929677841 Simplifying x = 511.929677841Subproblem 2
x + -256 = -255.929677841 Simplifying x + -256 = -255.929677841 Reorder the terms: -256 + x = -255.929677841 Solving -256 + x = -255.929677841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '256' to each side of the equation. -256 + 256 + x = -255.929677841 + 256 Combine like terms: -256 + 256 = 0 0 + x = -255.929677841 + 256 x = -255.929677841 + 256 Combine like terms: -255.929677841 + 256 = 0.070322159 x = 0.070322159 Simplifying x = 0.070322159Solution
The solution to the problem is based on the solutions from the subproblems. x = {511.929677841, 0.070322159}
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