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Simplifying 3x(x + 5) + 2x2 = 8x + -11 Reorder the terms: 3x(5 + x) + 2x2 = 8x + -11 (5 * 3x + x * 3x) + 2x2 = 8x + -11 (15x + 3x2) + 2x2 = 8x + -11 Combine like terms: 3x2 + 2x2 = 5x2 15x + 5x2 = 8x + -11 Reorder the terms: 15x + 5x2 = -11 + 8x Solving 15x + 5x2 = -11 + 8x Solving for variable 'x'. Reorder the terms: 11 + 15x + -8x + 5x2 = -11 + 8x + 11 + -8x Combine like terms: 15x + -8x = 7x 11 + 7x + 5x2 = -11 + 8x + 11 + -8x Reorder the terms: 11 + 7x + 5x2 = -11 + 11 + 8x + -8x Combine like terms: -11 + 11 = 0 11 + 7x + 5x2 = 0 + 8x + -8x 11 + 7x + 5x2 = 8x + -8x Combine like terms: 8x + -8x = 0 11 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.2 + 1.4x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + 1.4x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + 1.4x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + 1.4x + x2 = 0 + -2.2 1.4x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 1.4x + x2 = -2.2 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -2.2 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -2.2 + 0.49 Combine like terms: -2.2 + 0.49 = -1.71 0.49 + 1.4x + x2 = -1.71 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -1.71 Can't calculate square root of the right side. The solution to this equation could not be determined.
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