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Simplifying 56z2 + -2z + 22 = 0 Reorder the terms: 22 + -2z + 56z2 = 0 Solving 22 + -2z + 56z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -1z + 28z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -1z + 28z2)' equal to zero and attempt to solve: Simplifying 11 + -1z + 28z2 = 0 Solving 11 + -1z + 28z2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.3928571429 + -0.03571428571z + z2 = 0 Move the constant term to the right: Add '-0.3928571429' to each side of the equation. 0.3928571429 + -0.03571428571z + -0.3928571429 + z2 = 0 + -0.3928571429 Reorder the terms: 0.3928571429 + -0.3928571429 + -0.03571428571z + z2 = 0 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + -0.03571428571z + z2 = 0 + -0.3928571429 -0.03571428571z + z2 = 0 + -0.3928571429 Combine like terms: 0 + -0.3928571429 = -0.3928571429 -0.03571428571z + z2 = -0.3928571429 The z term is -0.03571428571z. Take half its coefficient (-0.01785714286). Square it (0.0003188775511) and add it to both sides. Add '0.0003188775511' to each side of the equation. -0.03571428571z + 0.0003188775511 + z2 = -0.3928571429 + 0.0003188775511 Reorder the terms: 0.0003188775511 + -0.03571428571z + z2 = -0.3928571429 + 0.0003188775511 Combine like terms: -0.3928571429 + 0.0003188775511 = -0.3925382653489 0.0003188775511 + -0.03571428571z + z2 = -0.3925382653489 Factor a perfect square on the left side: (z + -0.01785714286)(z + -0.01785714286) = -0.3925382653489 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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