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Simplifying x2 + -64x + 16 = 0 Reorder the terms: 16 + -64x + x2 = 0 Solving 16 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -64x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -64x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -64x + x2 = 0 + -16 -64x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -64x + x2 = -16 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 = -16 + 1024 Reorder the terms: 1024 + -64x + x2 = -16 + 1024 Combine like terms: -16 + 1024 = 1008 1024 + -64x + x2 = 1008 Factor a perfect square on the left side: (x + -32)(x + -32) = 1008 Calculate the square root of the right side: 31.749015733 Break this problem into two subproblems by setting (x + -32) equal to 31.749015733 and -31.749015733.Subproblem 1
x + -32 = 31.749015733 Simplifying x + -32 = 31.749015733 Reorder the terms: -32 + x = 31.749015733 Solving -32 + x = 31.749015733 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 = 31.749015733 + 32 Combine like terms: -32 + 32 = 0 0 + x = 31.749015733 + 32 x = 31.749015733 + 32 Combine like terms: 31.749015733 + 32 = 63.749015733 x = 63.749015733 Simplifying x = 63.749015733Subproblem 2
x + -32 = -31.749015733 Simplifying x + -32 = -31.749015733 Reorder the terms: -32 + x = -31.749015733 Solving -32 + x = -31.749015733 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 = -31.749015733 + 32 Combine like terms: -32 + 32 = 0 0 + x = -31.749015733 + 32 x = -31.749015733 + 32 Combine like terms: -31.749015733 + 32 = 0.250984267 x = 0.250984267 Simplifying x = 0.250984267Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.749015733, 0.250984267}
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