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Simplifying 2z2 + -20z + -50 = -512 Reorder the terms: -50 + -20z + 2z2 = -512 Solving -50 + -20z + 2z2 = -512 Solving for variable 'z'. Reorder the terms: -50 + 512 + -20z + 2z2 = -512 + 512 Combine like terms: -50 + 512 = 462 462 + -20z + 2z2 = -512 + 512 Combine like terms: -512 + 512 = 0 462 + -20z + 2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(231 + -10z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(231 + -10z + z2)' equal to zero and attempt to solve: Simplifying 231 + -10z + z2 = 0 Solving 231 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-231' to each side of the equation. 231 + -10z + -231 + z2 = 0 + -231 Reorder the terms: 231 + -231 + -10z + z2 = 0 + -231 Combine like terms: 231 + -231 = 0 0 + -10z + z2 = 0 + -231 -10z + z2 = 0 + -231 Combine like terms: 0 + -231 = -231 -10z + z2 = -231 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = -231 + 25 Reorder the terms: 25 + -10z + z2 = -231 + 25 Combine like terms: -231 + 25 = -206 25 + -10z + z2 = -206 Factor a perfect square on the left side: (z + -5)(z + -5) = -206 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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