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Simplifying x2 + -64(x + -2) = 0 Reorder the terms: x2 + -64(-2 + x) = 0 x2 + (-2 * -64 + x * -64) = 0 x2 + (128 + -64x) = 0 Reorder the terms: 128 + -64x + x2 = 0 Solving 128 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-128' to each side of the equation. 128 + -64x + -128 + x2 = 0 + -128 Reorder the terms: 128 + -128 + -64x + x2 = 0 + -128 Combine like terms: 128 + -128 = 0 0 + -64x + x2 = 0 + -128 -64x + x2 = 0 + -128 Combine like terms: 0 + -128 = -128 -64x + x2 = -128 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 = -128 + 1024 Reorder the terms: 1024 + -64x + x2 = -128 + 1024 Combine like terms: -128 + 1024 = 896 1024 + -64x + x2 = 896 Factor a perfect square on the left side: (x + -32)(x + -32) = 896 Calculate the square root of the right side: 29.933259094 Break this problem into two subproblems by setting (x + -32) equal to 29.933259094 and -29.933259094.Subproblem 1
x + -32 = 29.933259094 Simplifying x + -32 = 29.933259094 Reorder the terms: -32 + x = 29.933259094 Solving -32 + x = 29.933259094 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 = 29.933259094 + 32 Combine like terms: -32 + 32 = 0 0 + x = 29.933259094 + 32 x = 29.933259094 + 32 Combine like terms: 29.933259094 + 32 = 61.933259094 x = 61.933259094 Simplifying x = 61.933259094Subproblem 2
x + -32 = -29.933259094 Simplifying x + -32 = -29.933259094 Reorder the terms: -32 + x = -29.933259094 Solving -32 + x = -29.933259094 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 = -29.933259094 + 32 Combine like terms: -32 + 32 = 0 0 + x = -29.933259094 + 32 x = -29.933259094 + 32 Combine like terms: -29.933259094 + 32 = 2.066740906 x = 2.066740906 Simplifying x = 2.066740906Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.933259094, 2.066740906}
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