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Simplifying 4x2 + 13x + 27 = 7x + 6 Reorder the terms: 27 + 13x + 4x2 = 7x + 6 Reorder the terms: 27 + 13x + 4x2 = 6 + 7x Solving 27 + 13x + 4x2 = 6 + 7x Solving for variable 'x'. Reorder the terms: 27 + -6 + 13x + -7x + 4x2 = 6 + 7x + -6 + -7x Combine like terms: 27 + -6 = 21 21 + 13x + -7x + 4x2 = 6 + 7x + -6 + -7x Combine like terms: 13x + -7x = 6x 21 + 6x + 4x2 = 6 + 7x + -6 + -7x Reorder the terms: 21 + 6x + 4x2 = 6 + -6 + 7x + -7x Combine like terms: 6 + -6 = 0 21 + 6x + 4x2 = 0 + 7x + -7x 21 + 6x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 21 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 1.5x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 1.5x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 1.5x + x2 = 0 + -5.25 1.5x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 1.5x + x2 = -5.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -5.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -5.25 + 0.5625 Combine like terms: -5.25 + 0.5625 = -4.6875 0.5625 + 1.5x + x2 = -4.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -4.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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