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Simplifying 2z2 + 6z + 20 = 0 Reorder the terms: 20 + 6z + 2z2 = 0 Solving 20 + 6z + 2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 3z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 3z + z2)' equal to zero and attempt to solve: Simplifying 10 + 3z + z2 = 0 Solving 10 + 3z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 3z + -10 + z2 = 0 + -10 Reorder the terms: 10 + -10 + 3z + z2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3z + z2 = 0 + -10 3z + z2 = 0 + -10 Combine like terms: 0 + -10 = -10 3z + z2 = -10 The z term is 3z. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3z + 2.25 + z2 = -10 + 2.25 Reorder the terms: 2.25 + 3z + z2 = -10 + 2.25 Combine like terms: -10 + 2.25 = -7.75 2.25 + 3z + z2 = -7.75 Factor a perfect square on the left side: (z + 1.5)(z + 1.5) = -7.75 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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