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Simplifying x2 + -64x + -786 = 0 Reorder the terms: -786 + -64x + x2 = 0 Solving -786 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '786' to each side of the equation. -786 + -64x + 786 + x2 = 0 + 786 Reorder the terms: -786 + 786 + -64x + x2 = 0 + 786 Combine like terms: -786 + 786 = 0 0 + -64x + x2 = 0 + 786 -64x + x2 = 0 + 786 Combine like terms: 0 + 786 = 786 -64x + x2 = 786 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 = 786 + 1024 Reorder the terms: 1024 + -64x + x2 = 786 + 1024 Combine like terms: 786 + 1024 = 1810 1024 + -64x + x2 = 1810 Factor a perfect square on the left side: (x + -32)(x + -32) = 1810 Calculate the square root of the right side: 42.544094772 Break this problem into two subproblems by setting (x + -32) equal to 42.544094772 and -42.544094772.Subproblem 1
x + -32 = 42.544094772 Simplifying x + -32 = 42.544094772 Reorder the terms: -32 + x = 42.544094772 Solving -32 + x = 42.544094772 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 = 42.544094772 + 32 Combine like terms: -32 + 32 = 0 0 + x = 42.544094772 + 32 x = 42.544094772 + 32 Combine like terms: 42.544094772 + 32 = 74.544094772 x = 74.544094772 Simplifying x = 74.544094772Subproblem 2
x + -32 = -42.544094772 Simplifying x + -32 = -42.544094772 Reorder the terms: -32 + x = -42.544094772 Solving -32 + x = -42.544094772 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 = -42.544094772 + 32 Combine like terms: -32 + 32 = 0 0 + x = -42.544094772 + 32 x = -42.544094772 + 32 Combine like terms: -42.544094772 + 32 = -10.544094772 x = -10.544094772 Simplifying x = -10.544094772Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.544094772, -10.544094772}
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