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Simplifying 3x(x + 1) + 5 = 0 Reorder the terms: 3x(1 + x) + 5 = 0 (1 * 3x + x * 3x) + 5 = 0 (3x + 3x2) + 5 = 0 Reorder the terms: 5 + 3x + 3x2 = 0 Solving 5 + 3x + 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'. 1.666666667 + x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x + x2 = 0 + -1.666666667 x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 x + x2 = -1.666666667 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. + 0.25 + x2 = -1.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.666666667 + 0.25 Combine like terms: -1.666666667 + 0.25 = -1.416666667 1.25 + x2 = -1.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.416666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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