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Simplifying 2z4 + -13z2 + 36 = 0 Reorder the terms: 36 + -13z2 + 2z4 = 0 Solving 36 + -13z2 + 2z4 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + -6.5z2 + z4 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -6.5z2 + -18 + z4 = 0 + -18 Reorder the terms: 18 + -18 + -6.5z2 + z4 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -6.5z2 + z4 = 0 + -18 -6.5z2 + z4 = 0 + -18 Combine like terms: 0 + -18 = -18 -6.5z2 + z4 = -18 The z term is -6.5z2. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5z2 + 10.5625 + z4 = -18 + 10.5625 Reorder the terms: 10.5625 + -6.5z2 + z4 = -18 + 10.5625 Combine like terms: -18 + 10.5625 = -7.4375 10.5625 + -6.5z2 + z4 = -7.4375 Factor a perfect square on the left side: (z2 + -3.25)(z2 + -3.25) = -7.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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