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Simplifying 13x2 + 3x + 6 = 8x2 Reorder the terms: 6 + 3x + 13x2 = 8x2 Solving 6 + 3x + 13x2 = 8x2 Solving for variable 'x'. Combine like terms: 13x2 + -8x2 = 5x2 6 + 3x + 5x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 6 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 0.6x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 0.6x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 0.6x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 0.6x + x2 = 0 + -1.2 0.6x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 0.6x + x2 = -1.2 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -1.2 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -1.2 + 0.09 Combine like terms: -1.2 + 0.09 = -1.11 0.09 + 0.6x + x2 = -1.11 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = -1.11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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