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Simplifying 4x2 + 15x + 29 = 9x + 2 Reorder the terms: 29 + 15x + 4x2 = 9x + 2 Reorder the terms: 29 + 15x + 4x2 = 2 + 9x Solving 29 + 15x + 4x2 = 2 + 9x Solving for variable 'x'. Reorder the terms: 29 + -2 + 15x + -9x + 4x2 = 2 + 9x + -2 + -9x Combine like terms: 29 + -2 = 27 27 + 15x + -9x + 4x2 = 2 + 9x + -2 + -9x Combine like terms: 15x + -9x = 6x 27 + 6x + 4x2 = 2 + 9x + -2 + -9x Reorder the terms: 27 + 6x + 4x2 = 2 + -2 + 9x + -9x Combine like terms: 2 + -2 = 0 27 + 6x + 4x2 = 0 + 9x + -9x 27 + 6x + 4x2 = 9x + -9x Combine like terms: 9x + -9x = 0 27 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.75 + 1.5x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + 1.5x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + 1.5x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + 1.5x + x2 = 0 + -6.75 1.5x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 1.5x + x2 = -6.75 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 = -6.75 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -6.75 + 0.5625 Combine like terms: -6.75 + 0.5625 = -6.1875 0.5625 + 1.5x + x2 = -6.1875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -6.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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