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Simplifying x2 + -64x + 27 = 0 Reorder the terms: 27 + -64x + x2 = 0 Solving 27 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -64x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -64x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -64x + x2 = 0 + -27 -64x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -64x + x2 = -27 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = -27 + 1024 Reorder the terms: 1024 + -64x + x2 = -27 + 1024 Combine like terms: -27 + 1024 = 997 1024 + -64x + x2 = 997 Factor a perfect square on the left side: (x + -32)(x + -32) = 997 Calculate the square root of the right side: 31.575306808 Break this problem into two subproblems by setting (x + -32) equal to 31.575306808 and -31.575306808.Subproblem 1
x + -32 = 31.575306808 Simplifying x + -32 = 31.575306808 Reorder the terms: -32 + x = 31.575306808 Solving -32 + x = 31.575306808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 31.575306808 + 32 Combine like terms: -32 + 32 = 0 0 + x = 31.575306808 + 32 x = 31.575306808 + 32 Combine like terms: 31.575306808 + 32 = 63.575306808 x = 63.575306808 Simplifying x = 63.575306808Subproblem 2
x + -32 = -31.575306808 Simplifying x + -32 = -31.575306808 Reorder the terms: -32 + x = -31.575306808 Solving -32 + x = -31.575306808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -31.575306808 + 32 Combine like terms: -32 + 32 = 0 0 + x = -31.575306808 + 32 x = -31.575306808 + 32 Combine like terms: -31.575306808 + 32 = 0.424693192 x = 0.424693192 Simplifying x = 0.424693192Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.575306808, 0.424693192}
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