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Simplifying -1(7z(11z + 1)) = 1 + (3z + 3) Reorder the terms: -1(7z(1 + 11z)) = 1 + (3z + 3) -1((1 * 7z + 11z * 7z)) = 1 + (3z + 3) -1((7z + 77z2)) = 1 + (3z + 3) (7z * -1 + 77z2 * -1) = 1 + (3z + 3) (-7z + -77z2) = 1 + (3z + 3) Reorder the terms: -7z + -77z2 = 1 + (3 + 3z) Remove parenthesis around (3 + 3z) -7z + -77z2 = 1 + 3 + 3z Combine like terms: 1 + 3 = 4 -7z + -77z2 = 4 + 3z Solving -7z + -77z2 = 4 + 3z Solving for variable 'z'. Reorder the terms: -4 + -7z + -3z + -77z2 = 4 + 3z + -4 + -3z Combine like terms: -7z + -3z = -10z -4 + -10z + -77z2 = 4 + 3z + -4 + -3z Reorder the terms: -4 + -10z + -77z2 = 4 + -4 + 3z + -3z Combine like terms: 4 + -4 = 0 -4 + -10z + -77z2 = 0 + 3z + -3z -4 + -10z + -77z2 = 3z + -3z Combine like terms: 3z + -3z = 0 -4 + -10z + -77z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 10z + 77z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 10z + 77z2)' equal to zero and attempt to solve: Simplifying 4 + 10z + 77z2 = 0 Solving 4 + 10z + 77z2 = 0 Begin completing the square. Divide all terms by 77 the coefficient of the squared term: Divide each side by '77'. 0.05194805195 + 0.1298701299z + z2 = 0 Move the constant term to the right: Add '-0.05194805195' to each side of the equation. 0.05194805195 + 0.1298701299z + -0.05194805195 + z2 = 0 + -0.05194805195 Reorder the terms: 0.05194805195 + -0.05194805195 + 0.1298701299z + z2 = 0 + -0.05194805195 Combine like terms: 0.05194805195 + -0.05194805195 = 0.00000000000 0.00000000000 + 0.1298701299z + z2 = 0 + -0.05194805195 0.1298701299z + z2 = 0 + -0.05194805195 Combine like terms: 0 + -0.05194805195 = -0.05194805195 0.1298701299z + z2 = -0.05194805195 The z term is 0.1298701299z. Take half its coefficient (0.06493506495). Square it (0.004216562660) and add it to both sides. Add '0.004216562660' to each side of the equation. 0.1298701299z + 0.004216562660 + z2 = -0.05194805195 + 0.004216562660 Reorder the terms: 0.004216562660 + 0.1298701299z + z2 = -0.05194805195 + 0.004216562660 Combine like terms: -0.05194805195 + 0.004216562660 = -0.04773148929 0.004216562660 + 0.1298701299z + z2 = -0.04773148929 Factor a perfect square on the left side: (z + 0.06493506495)(z + 0.06493506495) = -0.04773148929 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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