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Simplifying -1x2 + 6x + -6 = 3x + 1 Reorder the terms: -6 + 6x + -1x2 = 3x + 1 Reorder the terms: -6 + 6x + -1x2 = 1 + 3x Solving -6 + 6x + -1x2 = 1 + 3x Solving for variable 'x'. Reorder the terms: -6 + -1 + 6x + -3x + -1x2 = 1 + 3x + -1 + -3x Combine like terms: -6 + -1 = -7 -7 + 6x + -3x + -1x2 = 1 + 3x + -1 + -3x Combine like terms: 6x + -3x = 3x -7 + 3x + -1x2 = 1 + 3x + -1 + -3x Reorder the terms: -7 + 3x + -1x2 = 1 + -1 + 3x + -3x Combine like terms: 1 + -1 = 0 -7 + 3x + -1x2 = 0 + 3x + -3x -7 + 3x + -1x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -7 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -3x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -3x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -3x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x + x2 = 0 + -7 -3x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -3x + x2 = -7 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 = -7 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -7 + 2.25 Combine like terms: -7 + 2.25 = -4.75 2.25 + -3x + x2 = -4.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -4.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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