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Simplifying x2 + -32x + 54 = 0 Reorder the terms: 54 + -32x + x2 = 0 Solving 54 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -32x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -32x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -32x + x2 = 0 + -54 -32x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -32x + x2 = -54 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 = -54 + 256 Reorder the terms: 256 + -32x + x2 = -54 + 256 Combine like terms: -54 + 256 = 202 256 + -32x + x2 = 202 Factor a perfect square on the left side: (x + -16)(x + -16) = 202 Calculate the square root of the right side: 14.212670404 Break this problem into two subproblems by setting (x + -16) equal to 14.212670404 and -14.212670404.Subproblem 1
x + -16 = 14.212670404 Simplifying x + -16 = 14.212670404 Reorder the terms: -16 + x = 14.212670404 Solving -16 + x = 14.212670404 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 = 14.212670404 + 16 Combine like terms: -16 + 16 = 0 0 + x = 14.212670404 + 16 x = 14.212670404 + 16 Combine like terms: 14.212670404 + 16 = 30.212670404 x = 30.212670404 Simplifying x = 30.212670404Subproblem 2
x + -16 = -14.212670404 Simplifying x + -16 = -14.212670404 Reorder the terms: -16 + x = -14.212670404 Solving -16 + x = -14.212670404 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 = -14.212670404 + 16 Combine like terms: -16 + 16 = 0 0 + x = -14.212670404 + 16 x = -14.212670404 + 16 Combine like terms: -14.212670404 + 16 = 1.787329596 x = 1.787329596 Simplifying x = 1.787329596Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.212670404, 1.787329596}
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