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Simplifying 0 = 4x2 + -33x + 80 Reorder the terms: 0 = 80 + -33x + 4x2 Solving 0 = 80 + -33x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + 33x + -4x2 = 80 + -33x + 4x2 + -80 + 33x + -4x2 Reorder the terms: -80 + 33x + -4x2 = 80 + -80 + -33x + 33x + 4x2 + -4x2 Combine like terms: 80 + -80 = 0 -80 + 33x + -4x2 = 0 + -33x + 33x + 4x2 + -4x2 -80 + 33x + -4x2 = -33x + 33x + 4x2 + -4x2 Combine like terms: -33x + 33x = 0 -80 + 33x + -4x2 = 0 + 4x2 + -4x2 -80 + 33x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -80 + 33x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 20 + -8.25x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -8.25x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -8.25x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -8.25x + x2 = 0 + -20 -8.25x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -8.25x + x2 = -20 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = -20 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -20 + 17.015625 Combine like terms: -20 + 17.015625 = -2.984375 17.015625 + -8.25x + x2 = -2.984375 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = -2.984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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