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Simplifying 3(4z2 + -4 + 1) + -11(2z + -1) + 10 = 0 Reorder the terms: 3(-4 + 1 + 4z2) + -11(2z + -1) + 10 = 0 Combine like terms: -4 + 1 = -3 3(-3 + 4z2) + -11(2z + -1) + 10 = 0 (-3 * 3 + 4z2 * 3) + -11(2z + -1) + 10 = 0 (-9 + 12z2) + -11(2z + -1) + 10 = 0 Reorder the terms: -9 + 12z2 + -11(-1 + 2z) + 10 = 0 -9 + 12z2 + (-1 * -11 + 2z * -11) + 10 = 0 -9 + 12z2 + (11 + -22z) + 10 = 0 Reorder the terms: -9 + 11 + 10 + -22z + 12z2 = 0 Combine like terms: -9 + 11 = 2 2 + 10 + -22z + 12z2 = 0 Combine like terms: 2 + 10 = 12 12 + -22z + 12z2 = 0 Solving 12 + -22z + 12z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -11z + 6z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -11z + 6z2)' equal to zero and attempt to solve: Simplifying 6 + -11z + 6z2 = 0 Solving 6 + -11z + 6z2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1 + -1.833333333z + z2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.833333333z + -1 + z2 = 0 + -1 Reorder the terms: 1 + -1 + -1.833333333z + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.833333333z + z2 = 0 + -1 -1.833333333z + z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.833333333z + z2 = -1 The z term is -1.833333333z. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333z + 0.8402777775 + z2 = -1 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333z + z2 = -1 + 0.8402777775 Combine like terms: -1 + 0.8402777775 = -0.1597222225 0.8402777775 + -1.833333333z + z2 = -0.1597222225 Factor a perfect square on the left side: (z + -0.9166666665)(z + -0.9166666665) = -0.1597222225 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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