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Simplifying (-3z2 + 8z + -12) + -1(8z2 + z) = 0 Reorder the terms: (-12 + 8z + -3z2) + -1(8z2 + z) = 0 Remove parenthesis around (-12 + 8z + -3z2) -12 + 8z + -3z2 + -1(8z2 + z) = 0 Reorder the terms: -12 + 8z + -3z2 + -1(z + 8z2) = 0 -12 + 8z + -3z2 + (z * -1 + 8z2 * -1) = 0 -12 + 8z + -3z2 + (-1z + -8z2) = 0 Reorder the terms: -12 + 8z + -1z + -3z2 + -8z2 = 0 Combine like terms: 8z + -1z = 7z -12 + 7z + -3z2 + -8z2 = 0 Combine like terms: -3z2 + -8z2 = -11z2 -12 + 7z + -11z2 = 0 Solving -12 + 7z + -11z2 = 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'. 1.090909091 + -0.6363636364z + z2 = 0 Move the constant term to the right: Add '-1.090909091' to each side of the equation. 1.090909091 + -0.6363636364z + -1.090909091 + z2 = 0 + -1.090909091 Reorder the terms: 1.090909091 + -1.090909091 + -0.6363636364z + z2 = 0 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + -0.6363636364z + z2 = 0 + -1.090909091 -0.6363636364z + z2 = 0 + -1.090909091 Combine like terms: 0 + -1.090909091 = -1.090909091 -0.6363636364z + z2 = -1.090909091 The z term is -0.6363636364z. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364z + 0.1012396694 + z2 = -1.090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364z + z2 = -1.090909091 + 0.1012396694 Combine like terms: -1.090909091 + 0.1012396694 = -0.9896694216 0.1012396694 + -0.6363636364z + z2 = -0.9896694216 Factor a perfect square on the left side: (z + -0.3181818182)(z + -0.3181818182) = -0.9896694216 Can't calculate square root of the right side. The solution to this equation could not be determined.
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