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Simplifying x2 + 64x + -6 = 0 Reorder the terms: -6 + 64x + x2 = 0 Solving -6 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 64x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 64x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 64x + x2 = 0 + 6 64x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 64x + x2 = 6 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 = 6 + 1024 Reorder the terms: 1024 + 64x + x2 = 6 + 1024 Combine like terms: 6 + 1024 = 1030 1024 + 64x + x2 = 1030 Factor a perfect square on the left side: (x + 32)(x + 32) = 1030 Calculate the square root of the right side: 32.093613072 Break this problem into two subproblems by setting (x + 32) equal to 32.093613072 and -32.093613072.Subproblem 1
x + 32 = 32.093613072 Simplifying x + 32 = 32.093613072 Reorder the terms: 32 + x = 32.093613072 Solving 32 + x = 32.093613072 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 = 32.093613072 + -32 Combine like terms: 32 + -32 = 0 0 + x = 32.093613072 + -32 x = 32.093613072 + -32 Combine like terms: 32.093613072 + -32 = 0.093613072 x = 0.093613072 Simplifying x = 0.093613072Subproblem 2
x + 32 = -32.093613072 Simplifying x + 32 = -32.093613072 Reorder the terms: 32 + x = -32.093613072 Solving 32 + x = -32.093613072 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 = -32.093613072 + -32 Combine like terms: 32 + -32 = 0 0 + x = -32.093613072 + -32 x = -32.093613072 + -32 Combine like terms: -32.093613072 + -32 = -64.093613072 x = -64.093613072 Simplifying x = -64.093613072Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.093613072, -64.093613072}
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