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Simplifying 3z2 + 45 = 18z Reorder the terms: 45 + 3z2 = 18z Solving 45 + 3z2 = 18z Solving for variable 'z'. Reorder the terms: 45 + -18z + 3z2 = 18z + -18z Combine like terms: 18z + -18z = 0 45 + -18z + 3z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + -6z + z2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + -6z + z2)' equal to zero and attempt to solve: Simplifying 15 + -6z + z2 = 0 Solving 15 + -6z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -6z + -15 + z2 = 0 + -15 Reorder the terms: 15 + -15 + -6z + z2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -6z + z2 = 0 + -15 -6z + z2 = 0 + -15 Combine like terms: 0 + -15 = -15 -6z + z2 = -15 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 = -15 + 9 Reorder the terms: 9 + -6z + z2 = -15 + 9 Combine like terms: -15 + 9 = -6 9 + -6z + z2 = -6 Factor a perfect square on the left side: (z + -3)(z + -3) = -6 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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