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Simplifying 2z2 + 40 = -8z Reorder the terms: 40 + 2z2 = -8z Solving 40 + 2z2 = -8z Solving for variable 'z'. Reorder the terms: 40 + 8z + 2z2 = -8z + 8z Combine like terms: -8z + 8z = 0 40 + 8z + 2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 4z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 4z + z2)' equal to zero and attempt to solve: Simplifying 20 + 4z + z2 = 0 Solving 20 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 4z + -20 + z2 = 0 + -20 Reorder the terms: 20 + -20 + 4z + z2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 4z + z2 = 0 + -20 4z + z2 = 0 + -20 Combine like terms: 0 + -20 = -20 4z + z2 = -20 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = -20 + 4 Reorder the terms: 4 + 4z + z2 = -20 + 4 Combine like terms: -20 + 4 = -16 4 + 4z + z2 = -16 Factor a perfect square on the left side: (z + 2)(z + 2) = -16 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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