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Simplifying 6x = 2x2 + 7 Reorder the terms: 6x = 7 + 2x2 Solving 6x = 7 + 2x2 Solving for variable 'x'. Reorder the terms: -7 + 6x + -2x2 = 7 + 2x2 + -7 + -2x2 Reorder the terms: -7 + 6x + -2x2 = 7 + -7 + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -7 + 6x + -2x2 = 0 + 2x2 + -2x2 -7 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -7 + 6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3.5 + -3x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -3x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -3x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -3x + x2 = 0 + -3.5 -3x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -3x + x2 = -3.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -3.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -3.5 + 2.25 Combine like terms: -3.5 + 2.25 = -1.25 2.25 + -3x + x2 = -1.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -1.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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