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Simplifying 0 = 4x2 + -6x + 17 Reorder the terms: 0 = 17 + -6x + 4x2 Solving 0 = 17 + -6x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + 6x + -4x2 = 17 + -6x + 4x2 + -17 + 6x + -4x2 Reorder the terms: -17 + 6x + -4x2 = 17 + -17 + -6x + 6x + 4x2 + -4x2 Combine like terms: 17 + -17 = 0 -17 + 6x + -4x2 = 0 + -6x + 6x + 4x2 + -4x2 -17 + 6x + -4x2 = -6x + 6x + 4x2 + -4x2 Combine like terms: -6x + 6x = 0 -17 + 6x + -4x2 = 0 + 4x2 + -4x2 -17 + 6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -17 + 6x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 4.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -1.5x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -1.5x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -1.5x + x2 = 0 + -4.25 -1.5x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -1.5x + x2 = -4.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -4.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -4.25 + 0.5625 Combine like terms: -4.25 + 0.5625 = -3.6875 0.5625 + -1.5x + x2 = -3.6875 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -3.6875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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