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Simplifying x2 + 64x = -2 Reorder the terms: 64x + x2 = -2 Solving 64x + x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 64x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 64x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 64x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 64x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 64x + x2 = 0 + -2 64x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 64x + x2 = -2 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 = -2 + 1024 Reorder the terms: 1024 + 64x + x2 = -2 + 1024 Combine like terms: -2 + 1024 = 1022 1024 + 64x + x2 = 1022 Factor a perfect square on the left side: (x + 32)(x + 32) = 1022 Calculate the square root of the right side: 31.968734726 Break this problem into two subproblems by setting (x + 32) equal to 31.968734726 and -31.968734726.Subproblem 1
x + 32 = 31.968734726 Simplifying x + 32 = 31.968734726 Reorder the terms: 32 + x = 31.968734726 Solving 32 + x = 31.968734726 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 = 31.968734726 + -32 Combine like terms: 32 + -32 = 0 0 + x = 31.968734726 + -32 x = 31.968734726 + -32 Combine like terms: 31.968734726 + -32 = -0.031265274 x = -0.031265274 Simplifying x = -0.031265274Subproblem 2
x + 32 = -31.968734726 Simplifying x + 32 = -31.968734726 Reorder the terms: 32 + x = -31.968734726 Solving 32 + x = -31.968734726 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 = -31.968734726 + -32 Combine like terms: 32 + -32 = 0 0 + x = -31.968734726 + -32 x = -31.968734726 + -32 Combine like terms: -31.968734726 + -32 = -63.968734726 x = -63.968734726 Simplifying x = -63.968734726Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.031265274, -63.968734726}
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