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Simplifying 3x2 + 27x + 74 = 0 Reorder the terms: 74 + 27x + 3x2 = 0 Solving 74 + 27x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 24.66666667 + 9x + x2 = 0 Move the constant term to the right: Add '-24.66666667' to each side of the equation. 24.66666667 + 9x + -24.66666667 + x2 = 0 + -24.66666667 Reorder the terms: 24.66666667 + -24.66666667 + 9x + x2 = 0 + -24.66666667 Combine like terms: 24.66666667 + -24.66666667 = 0.00000000 0.00000000 + 9x + x2 = 0 + -24.66666667 9x + x2 = 0 + -24.66666667 Combine like terms: 0 + -24.66666667 = -24.66666667 9x + x2 = -24.66666667 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -24.66666667 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -24.66666667 + 20.25 Combine like terms: -24.66666667 + 20.25 = -4.41666667 20.25 + 9x + x2 = -4.41666667 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -4.41666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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