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Simplifying 16z2 + 61 = 6z Reorder the terms: 61 + 16z2 = 6z Solving 61 + 16z2 = 6z Solving for variable 'z'. Reorder the terms: 61 + -6z + 16z2 = 6z + -6z Combine like terms: 6z + -6z = 0 61 + -6z + 16z2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.8125 + -0.375z + z2 = 0 Move the constant term to the right: Add '-3.8125' to each side of the equation. 3.8125 + -0.375z + -3.8125 + z2 = 0 + -3.8125 Reorder the terms: 3.8125 + -3.8125 + -0.375z + z2 = 0 + -3.8125 Combine like terms: 3.8125 + -3.8125 = 0.0000 0.0000 + -0.375z + z2 = 0 + -3.8125 -0.375z + z2 = 0 + -3.8125 Combine like terms: 0 + -3.8125 = -3.8125 -0.375z + z2 = -3.8125 The z term is -0.375z. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375z + 0.03515625 + z2 = -3.8125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375z + z2 = -3.8125 + 0.03515625 Combine like terms: -3.8125 + 0.03515625 = -3.77734375 0.03515625 + -0.375z + z2 = -3.77734375 Factor a perfect square on the left side: (z + -0.1875)(z + -0.1875) = -3.77734375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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