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Simplifying (5x2 + -3x + -3) + -1(3x2 + -6x + -8) = 0 Reorder the terms: (-3 + -3x + 5x2) + -1(3x2 + -6x + -8) = 0 Remove parenthesis around (-3 + -3x + 5x2) -3 + -3x + 5x2 + -1(3x2 + -6x + -8) = 0 Reorder the terms: -3 + -3x + 5x2 + -1(-8 + -6x + 3x2) = 0 -3 + -3x + 5x2 + (-8 * -1 + -6x * -1 + 3x2 * -1) = 0 -3 + -3x + 5x2 + (8 + 6x + -3x2) = 0 Reorder the terms: -3 + 8 + -3x + 6x + 5x2 + -3x2 = 0 Combine like terms: -3 + 8 = 5 5 + -3x + 6x + 5x2 + -3x2 = 0 Combine like terms: -3x + 6x = 3x 5 + 3x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 5 + 3x + 2x2 = 0 Solving 5 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.5x + x2 = 0 + -2.5 1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.5x + x2 = -2.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + 1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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