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Simplifying 32x2 + x + 65 = 0 Reorder the terms: 65 + x + 32x2 = 0 Solving 65 + x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 2.03125 + 0.03125x + x2 = 0 Move the constant term to the right: Add '-2.03125' to each side of the equation. 2.03125 + 0.03125x + -2.03125 + x2 = 0 + -2.03125 Reorder the terms: 2.03125 + -2.03125 + 0.03125x + x2 = 0 + -2.03125 Combine like terms: 2.03125 + -2.03125 = 0.00000 0.00000 + 0.03125x + x2 = 0 + -2.03125 0.03125x + x2 = 0 + -2.03125 Combine like terms: 0 + -2.03125 = -2.03125 0.03125x + x2 = -2.03125 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.03125x + 0.25 + x2 = -2.03125 + 0.25 Reorder the terms: 0.25 + 0.03125x + x2 = -2.03125 + 0.25 Combine like terms: -2.03125 + 0.25 = -1.78125 0.25 + 0.03125x + x2 = -1.78125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.78125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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