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Simplifying 3x2 + 15x + 32 = 0 Reorder the terms: 32 + 15x + 3x2 = 0 Solving 32 + 15x + 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'. 10.66666667 + 5x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + 5x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + 5x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + 5x + x2 = 0 + -10.66666667 5x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 5x + x2 = -10.66666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -10.66666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -10.66666667 + 6.25 Combine like terms: -10.66666667 + 6.25 = -4.41666667 6.25 + 5x + x2 = -4.41666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -4.41666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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