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Simplifying 2x2 + 7x + 13 = 6x Reorder the terms: 13 + 7x + 2x2 = 6x Solving 13 + 7x + 2x2 = 6x Solving for variable 'x'. Reorder the terms: 13 + 7x + -6x + 2x2 = 6x + -6x Combine like terms: 7x + -6x = 1x 13 + 1x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 13 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 0.5x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 0.5x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 0.5x + x2 = 0 + -6.5 0.5x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 0.5x + x2 = -6.5 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 = -6.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -6.5 + 0.0625 Combine like terms: -6.5 + 0.0625 = -6.4375 0.0625 + 0.5x + x2 = -6.4375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -6.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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