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Simplifying 5z2 + 5z + 10 = 0 Reorder the terms: 10 + 5z + 5z2 = 0 Solving 10 + 5z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + z + z2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + z + z2)' equal to zero and attempt to solve: Simplifying 2 + z + z2 = 0 Solving 2 + z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z + z2 = 0 + -2 z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 z + z2 = -2 The z term is z. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. z + 0.25 + z2 = -2 + 0.25 Reorder the terms: 0.25 + z + z2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + z + z2 = -1.75 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = -1.75 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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