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Simplifying F(0) = 4x2 + -9x + 8 Reorder the terms for easier multiplication: 0F = 4x2 + -9x + 8 Anything times zero is zero. 0F = 4x2 + -9x + 8 Reorder the terms: 0 = 8 + -9x + 4x2 Solving 0 = 8 + -9x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 9x + -4x2 = 8 + -9x + 4x2 + -8 + 9x + -4x2 Reorder the terms: -8 + 9x + -4x2 = 8 + -8 + -9x + 9x + 4x2 + -4x2 Combine like terms: 8 + -8 = 0 -8 + 9x + -4x2 = 0 + -9x + 9x + 4x2 + -4x2 -8 + 9x + -4x2 = -9x + 9x + 4x2 + -4x2 Combine like terms: -9x + 9x = 0 -8 + 9x + -4x2 = 0 + 4x2 + -4x2 -8 + 9x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8 + 9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2 + -2.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.25x + x2 = 0 + -2 -2.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.25x + x2 = -2 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -2 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -2 + 1.265625 Combine like terms: -2 + 1.265625 = -0.734375 1.265625 + -2.25x + x2 = -0.734375 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = -0.734375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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