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Simplifying 12z = 7z2 + 20 Reorder the terms: 12z = 20 + 7z2 Solving 12z = 20 + 7z2 Solving for variable 'z'. Reorder the terms: -20 + 12z + -7z2 = 20 + 7z2 + -20 + -7z2 Reorder the terms: -20 + 12z + -7z2 = 20 + -20 + 7z2 + -7z2 Combine like terms: 20 + -20 = 0 -20 + 12z + -7z2 = 0 + 7z2 + -7z2 -20 + 12z + -7z2 = 7z2 + -7z2 Combine like terms: 7z2 + -7z2 = 0 -20 + 12z + -7z2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 2.857142857 + -1.714285714z + z2 = 0 Move the constant term to the right: Add '-2.857142857' to each side of the equation. 2.857142857 + -1.714285714z + -2.857142857 + z2 = 0 + -2.857142857 Reorder the terms: 2.857142857 + -2.857142857 + -1.714285714z + z2 = 0 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + -1.714285714z + z2 = 0 + -2.857142857 -1.714285714z + z2 = 0 + -2.857142857 Combine like terms: 0 + -2.857142857 = -2.857142857 -1.714285714z + z2 = -2.857142857 The z term is -1.714285714z. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714z + 0.7346938773 + z2 = -2.857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714z + z2 = -2.857142857 + 0.7346938773 Combine like terms: -2.857142857 + 0.7346938773 = -2.1224489797 0.7346938773 + -1.714285714z + z2 = -2.1224489797 Factor a perfect square on the left side: (z + -0.857142857)(z + -0.857142857) = -2.1224489797 Can't calculate square root of the right side. The solution to this equation could not be determined.
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