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Simplifying -3z2 + 3z = 23 Reorder the terms: 3z + -3z2 = 23 Solving 3z + -3z2 = 23 Solving for variable 'z'. Reorder the terms: -23 + 3z + -3z2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 3z + -3z2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 7.666666667 + -1z + z2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + -1z + -7.666666667 + z2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + -1z + z2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + -1z + z2 = 0 + -7.666666667 -1z + z2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 -1z + z2 = -7.666666667 The z term is -1z. 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. -1z + 0.25 + z2 = -7.666666667 + 0.25 Reorder the terms: 0.25 + -1z + z2 = -7.666666667 + 0.25 Combine like terms: -7.666666667 + 0.25 = -7.416666667 0.25 + -1z + z2 = -7.416666667 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = -7.416666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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