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Simplifying (3 + 5x)(2 + -3x) = 12 + -1(5x) * 2 Multiply (3 + 5x) * (2 + -3x) (3(2 + -3x) + 5x * (2 + -3x)) = 12 + -1(5x) * 2 ((2 * 3 + -3x * 3) + 5x * (2 + -3x)) = 12 + -1(5x) * 2 ((6 + -9x) + 5x * (2 + -3x)) = 12 + -1(5x) * 2 (6 + -9x + (2 * 5x + -3x * 5x)) = 12 + -1(5x) * 2 (6 + -9x + (10x + -15x2)) = 12 + -1(5x) * 2 Combine like terms: -9x + 10x = 1x (6 + 1x + -15x2) = 12 + -1(5x) * 2 Remove parenthesis around (5x) 6 + 1x + -15x2 = 12 + -1 * 5x * 2 Reorder the terms for easier multiplication: 6 + 1x + -15x2 = 12 + -1 * 5 * 2x Multiply -1 * 5 6 + 1x + -15x2 = 12 + -5 * 2x Multiply -5 * 2 6 + 1x + -15x2 = 12 + -10x Solving 6 + 1x + -15x2 = 12 + -10x Solving for variable 'x'. Reorder the terms: 6 + -12 + 1x + 10x + -15x2 = 12 + -10x + -12 + 10x Combine like terms: 6 + -12 = -6 -6 + 1x + 10x + -15x2 = 12 + -10x + -12 + 10x Combine like terms: 1x + 10x = 11x -6 + 11x + -15x2 = 12 + -10x + -12 + 10x Reorder the terms: -6 + 11x + -15x2 = 12 + -12 + -10x + 10x Combine like terms: 12 + -12 = 0 -6 + 11x + -15x2 = 0 + -10x + 10x -6 + 11x + -15x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -6 + 11x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 0.4 + -0.7333333333x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.7333333333x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.7333333333x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.7333333333x + x2 = 0 + -0.4 -0.7333333333x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.7333333333x + x2 = -0.4 The x term is -0.7333333333x. Take half its coefficient (-0.3666666667). Square it (0.1344444445) and add it to both sides. Add '0.1344444445' to each side of the equation. -0.7333333333x + 0.1344444445 + x2 = -0.4 + 0.1344444445 Reorder the terms: 0.1344444445 + -0.7333333333x + x2 = -0.4 + 0.1344444445 Combine like terms: -0.4 + 0.1344444445 = -0.2655555555 0.1344444445 + -0.7333333333x + x2 = -0.2655555555 Factor a perfect square on the left side: (x + -0.3666666667)(x + -0.3666666667) = -0.2655555555 Can't calculate square root of the right side. The solution to this equation could not be determined.
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