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Simplifying 12z + -2z2 = 36 Solving 12z + -2z2 = 36 Solving for variable 'z'. Reorder the terms: -36 + 12z + -2z2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 12z + -2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 6z + -1z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 6z + -1z2)' equal to zero and attempt to solve: Simplifying -18 + 6z + -1z2 = 0 Solving -18 + 6z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -6z + z2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -6z + -18 + z2 = 0 + -18 Reorder the terms: 18 + -18 + -6z + z2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -6z + z2 = 0 + -18 -6z + z2 = 0 + -18 Combine like terms: 0 + -18 = -18 -6z + z2 = -18 The z term is -6z. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6z + 9 + z2 = -18 + 9 Reorder the terms: 9 + -6z + z2 = -18 + 9 Combine like terms: -18 + 9 = -9 9 + -6z + z2 = -9 Factor a perfect square on the left side: (z + -3)(z + -3) = -9 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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