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Simplifying x2 + -256x + 15 = 0 Reorder the terms: 15 + -256x + x2 = 0 Solving 15 + -256x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -256x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -256x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -256x + x2 = 0 + -15 -256x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -256x + x2 = -15 The x term is -256x. Take half its coefficient (-128). Square it (16384) and add it to both sides. Add '16384' to each side of the equation. -256x + 16384 + x2 = -15 + 16384 Reorder the terms: 16384 + -256x + x2 = -15 + 16384 Combine like terms: -15 + 16384 = 16369 16384 + -256x + x2 = 16369 Factor a perfect square on the left side: (x + -128)(x + -128) = 16369 Calculate the square root of the right side: 127.941392833 Break this problem into two subproblems by setting (x + -128) equal to 127.941392833 and -127.941392833.Subproblem 1
x + -128 = 127.941392833 Simplifying x + -128 = 127.941392833 Reorder the terms: -128 + x = 127.941392833 Solving -128 + x = 127.941392833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '128' to each side of the equation. -128 + 128 + x = 127.941392833 + 128 Combine like terms: -128 + 128 = 0 0 + x = 127.941392833 + 128 x = 127.941392833 + 128 Combine like terms: 127.941392833 + 128 = 255.941392833 x = 255.941392833 Simplifying x = 255.941392833Subproblem 2
x + -128 = -127.941392833 Simplifying x + -128 = -127.941392833 Reorder the terms: -128 + x = -127.941392833 Solving -128 + x = -127.941392833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '128' to each side of the equation. -128 + 128 + x = -127.941392833 + 128 Combine like terms: -128 + 128 = 0 0 + x = -127.941392833 + 128 x = -127.941392833 + 128 Combine like terms: -127.941392833 + 128 = 0.058607167 x = 0.058607167 Simplifying x = 0.058607167Solution
The solution to the problem is based on the solutions from the subproblems. x = {255.941392833, 0.058607167}
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