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Simplifying 5x(3x + 4) + -2x = 7x + -3(-2x + 11) Reorder the terms: 5x(4 + 3x) + -2x = 7x + -3(-2x + 11) (4 * 5x + 3x * 5x) + -2x = 7x + -3(-2x + 11) (20x + 15x2) + -2x = 7x + -3(-2x + 11) Reorder the terms: 20x + -2x + 15x2 = 7x + -3(-2x + 11) Combine like terms: 20x + -2x = 18x 18x + 15x2 = 7x + -3(-2x + 11) Reorder the terms: 18x + 15x2 = 7x + -3(11 + -2x) 18x + 15x2 = 7x + (11 * -3 + -2x * -3) 18x + 15x2 = 7x + (-33 + 6x) Reorder the terms: 18x + 15x2 = -33 + 7x + 6x Combine like terms: 7x + 6x = 13x 18x + 15x2 = -33 + 13x Solving 18x + 15x2 = -33 + 13x Solving for variable 'x'. Reorder the terms: 33 + 18x + -13x + 15x2 = -33 + 13x + 33 + -13x Combine like terms: 18x + -13x = 5x 33 + 5x + 15x2 = -33 + 13x + 33 + -13x Reorder the terms: 33 + 5x + 15x2 = -33 + 33 + 13x + -13x Combine like terms: -33 + 33 = 0 33 + 5x + 15x2 = 0 + 13x + -13x 33 + 5x + 15x2 = 13x + -13x Combine like terms: 13x + -13x = 0 33 + 5x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 2.2 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + 0.3333333333x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + 0.3333333333x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + 0.3333333333x + x2 = 0 + -2.2 0.3333333333x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 0.3333333333x + x2 = -2.2 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -2.2 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -2.2 + 0.02777777779 Combine like terms: -2.2 + 0.02777777779 = -2.17222222221 0.02777777779 + 0.3333333333x + x2 = -2.17222222221 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -2.17222222221 Can't calculate square root of the right side. The solution to this equation could not be determined.
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