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Simplifying P(0) = 3x2 + -3x + 1 Reorder the terms for easier multiplication: 0P = 3x2 + -3x + 1 Anything times zero is zero. 0P = 3x2 + -3x + 1 Reorder the terms: 0 = 1 + -3x + 3x2 Solving 0 = 1 + -3x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 3x + -3x2 = 1 + -3x + 3x2 + -1 + 3x + -3x2 Reorder the terms: -1 + 3x + -3x2 = 1 + -1 + -3x + 3x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 -1 + 3x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2 -1 + 3x + -3x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 -1 + 3x + -3x2 = 0 + 3x2 + -3x2 -1 + 3x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1 + 3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.3333333333 -1x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1x + x2 = -0.3333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + -1x + x2 = -0.0833333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.0833333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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