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Simplifying 3x2 + 24x + 53 = 0 Reorder the terms: 53 + 24x + 3x2 = 0 Solving 53 + 24x + 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'. 17.66666667 + 8x + x2 = 0 Move the constant term to the right: Add '-17.66666667' to each side of the equation. 17.66666667 + 8x + -17.66666667 + x2 = 0 + -17.66666667 Reorder the terms: 17.66666667 + -17.66666667 + 8x + x2 = 0 + -17.66666667 Combine like terms: 17.66666667 + -17.66666667 = 0.00000000 0.00000000 + 8x + x2 = 0 + -17.66666667 8x + x2 = 0 + -17.66666667 Combine like terms: 0 + -17.66666667 = -17.66666667 8x + x2 = -17.66666667 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -17.66666667 + 16 Reorder the terms: 16 + 8x + x2 = -17.66666667 + 16 Combine like terms: -17.66666667 + 16 = -1.66666667 16 + 8x + x2 = -1.66666667 Factor a perfect square on the left side: (x + 4)(x + 4) = -1.66666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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