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Simplifying 4x2 + 14x = 12x + -5 Reorder the terms: 14x + 4x2 = 12x + -5 Reorder the terms: 14x + 4x2 = -5 + 12x Solving 14x + 4x2 = -5 + 12x Solving for variable 'x'. Reorder the terms: 5 + 14x + -12x + 4x2 = -5 + 12x + 5 + -12x Combine like terms: 14x + -12x = 2x 5 + 2x + 4x2 = -5 + 12x + 5 + -12x Reorder the terms: 5 + 2x + 4x2 = -5 + 5 + 12x + -12x Combine like terms: -5 + 5 = 0 5 + 2x + 4x2 = 0 + 12x + -12x 5 + 2x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 5 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.5x + x2 = 0 + -1.25 0.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.5x + x2 = -1.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + 0.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -1.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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