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Simplifying x2 + 4 + -32x = 0 Reorder the terms: 4 + -32x + x2 = 0 Solving 4 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -32x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -32x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -32x + x2 = 0 + -4 -32x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -32x + x2 = -4 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -4 + 256 Reorder the terms: 256 + -32x + x2 = -4 + 256 Combine like terms: -4 + 256 = 252 256 + -32x + x2 = 252 Factor a perfect square on the left side: (x + -16)(x + -16) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -16) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -16 = 15.874507866 Simplifying x + -16 = 15.874507866 Reorder the terms: -16 + x = 15.874507866 Solving -16 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 15.874507866 + 16 Combine like terms: -16 + 16 = 0 0 + x = 15.874507866 + 16 x = 15.874507866 + 16 Combine like terms: 15.874507866 + 16 = 31.874507866 x = 31.874507866 Simplifying x = 31.874507866Subproblem 2
x + -16 = -15.874507866 Simplifying x + -16 = -15.874507866 Reorder the terms: -16 + x = -15.874507866 Solving -16 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -15.874507866 + 16 Combine like terms: -16 + 16 = 0 0 + x = -15.874507866 + 16 x = -15.874507866 + 16 Combine like terms: -15.874507866 + 16 = 0.125492134 x = 0.125492134 Simplifying x = 0.125492134Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.874507866, 0.125492134}
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