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Simplifying 2z2 + -18z = -72 Reorder the terms: -18z + 2z2 = -72 Solving -18z + 2z2 = -72 Solving for variable 'z'. Reorder the terms: 72 + -18z + 2z2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + -18z + 2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -9z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + -9z + z2)' equal to zero and attempt to solve: Simplifying 36 + -9z + z2 = 0 Solving 36 + -9z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -9z + -36 + z2 = 0 + -36 Reorder the terms: 36 + -36 + -9z + z2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -9z + z2 = 0 + -36 -9z + z2 = 0 + -36 Combine like terms: 0 + -36 = -36 -9z + z2 = -36 The z term is -9z. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9z + 20.25 + z2 = -36 + 20.25 Reorder the terms: 20.25 + -9z + z2 = -36 + 20.25 Combine like terms: -36 + 20.25 = -15.75 20.25 + -9z + z2 = -15.75 Factor a perfect square on the left side: (z + -4.5)(z + -4.5) = -15.75 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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