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Simplifying 220z2 + -140z + 245 = 0 Reorder the terms: 245 + -140z + 220z2 = 0 Solving 245 + -140z + 220z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(49 + -28z + 44z2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(49 + -28z + 44z2)' equal to zero and attempt to solve: Simplifying 49 + -28z + 44z2 = 0 Solving 49 + -28z + 44z2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. 1.113636364 + -0.6363636364z + z2 = 0 Move the constant term to the right: Add '-1.113636364' to each side of the equation. 1.113636364 + -0.6363636364z + -1.113636364 + z2 = 0 + -1.113636364 Reorder the terms: 1.113636364 + -1.113636364 + -0.6363636364z + z2 = 0 + -1.113636364 Combine like terms: 1.113636364 + -1.113636364 = 0.000000000 0.000000000 + -0.6363636364z + z2 = 0 + -1.113636364 -0.6363636364z + z2 = 0 + -1.113636364 Combine like terms: 0 + -1.113636364 = -1.113636364 -0.6363636364z + z2 = -1.113636364 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 = -1.113636364 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364z + z2 = -1.113636364 + 0.1012396694 Combine like terms: -1.113636364 + 0.1012396694 = -1.0123966946 0.1012396694 + -0.6363636364z + z2 = -1.0123966946 Factor a perfect square on the left side: (z + -0.3181818182)(z + -0.3181818182) = -1.0123966946 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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