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Simplifying 5x(2x + -3) + 3(x + 5) = 11x + -3 Reorder the terms: 5x(-3 + 2x) + 3(x + 5) = 11x + -3 (-3 * 5x + 2x * 5x) + 3(x + 5) = 11x + -3 (-15x + 10x2) + 3(x + 5) = 11x + -3 Reorder the terms: -15x + 10x2 + 3(5 + x) = 11x + -3 -15x + 10x2 + (5 * 3 + x * 3) = 11x + -3 -15x + 10x2 + (15 + 3x) = 11x + -3 Reorder the terms: 15 + -15x + 3x + 10x2 = 11x + -3 Combine like terms: -15x + 3x = -12x 15 + -12x + 10x2 = 11x + -3 Reorder the terms: 15 + -12x + 10x2 = -3 + 11x Solving 15 + -12x + 10x2 = -3 + 11x Solving for variable 'x'. Reorder the terms: 15 + 3 + -12x + -11x + 10x2 = -3 + 11x + 3 + -11x Combine like terms: 15 + 3 = 18 18 + -12x + -11x + 10x2 = -3 + 11x + 3 + -11x Combine like terms: -12x + -11x = -23x 18 + -23x + 10x2 = -3 + 11x + 3 + -11x Reorder the terms: 18 + -23x + 10x2 = -3 + 3 + 11x + -11x Combine like terms: -3 + 3 = 0 18 + -23x + 10x2 = 0 + 11x + -11x 18 + -23x + 10x2 = 11x + -11x Combine like terms: 11x + -11x = 0 18 + -23x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.8 + -2.3x + x2 = 0.0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -2.3x + -1.8 + x2 = 0.0 + -1.8 Reorder the terms: 1.8 + -1.8 + -2.3x + x2 = 0.0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -2.3x + x2 = 0.0 + -1.8 -2.3x + x2 = 0.0 + -1.8 Combine like terms: 0.0 + -1.8 = -1.8 -2.3x + x2 = -1.8 The x term is -2.3x. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3x + 1.3225 + x2 = -1.8 + 1.3225 Reorder the terms: 1.3225 + -2.3x + x2 = -1.8 + 1.3225 Combine like terms: -1.8 + 1.3225 = -0.4775 1.3225 + -2.3x + x2 = -0.4775 Factor a perfect square on the left side: (x + -1.15)(x + -1.15) = -0.4775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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