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Simplifying 11z4 + -11z2 + 3 = 0 Reorder the terms: 3 + -11z2 + 11z4 = 0 Solving 3 + -11z2 + 11z4 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.2727272727 + -1z2 + z4 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + -1z2 + -0.2727272727 + z4 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + -1z2 + z4 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + -1z2 + z4 = 0 + -0.2727272727 -1z2 + z4 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 -1z2 + z4 = -0.2727272727 The z term is -1z2. 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. -1z2 + 0.25 + z4 = -0.2727272727 + 0.25 Reorder the terms: 0.25 + -1z2 + z4 = -0.2727272727 + 0.25 Combine like terms: -0.2727272727 + 0.25 = -0.0227272727 0.25 + -1z2 + z4 = -0.0227272727 Factor a perfect square on the left side: (z2 + -0.5)(z2 + -0.5) = -0.0227272727 Can't calculate square root of the right side. The solution to this equation could not be determined.
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