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Simplifying 3x2 + 7x + 11 = 5x + 7 Reorder the terms: 11 + 7x + 3x2 = 5x + 7 Reorder the terms: 11 + 7x + 3x2 = 7 + 5x Solving 11 + 7x + 3x2 = 7 + 5x Solving for variable 'x'. Reorder the terms: 11 + -7 + 7x + -5x + 3x2 = 7 + 5x + -7 + -5x Combine like terms: 11 + -7 = 4 4 + 7x + -5x + 3x2 = 7 + 5x + -7 + -5x Combine like terms: 7x + -5x = 2x 4 + 2x + 3x2 = 7 + 5x + -7 + -5x Reorder the terms: 4 + 2x + 3x2 = 7 + -7 + 5x + -5x Combine like terms: 7 + -7 = 0 4 + 2x + 3x2 = 0 + 5x + -5x 4 + 2x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 4 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.6666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + -1.333333333 0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.6666666667x + x2 = -1.333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + 0.6666666667x + x2 = -1.2222222218 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -1.2222222218 Can't calculate square root of the right side. The solution to this equation could not be determined.
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