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Simplifying -4z2 + -4z + -3 = 0 Reorder the terms: -3 + -4z + -4z2 = 0 Solving -3 + -4z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 4z + 4z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 4z + 4z2)' equal to zero and attempt to solve: Simplifying 3 + 4z + 4z2 = 0 Solving 3 + 4z + 4z2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + z + z2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + z + -0.75 + z2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + z + z2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + z + z2 = 0 + -0.75 z + z2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 z + z2 = -0.75 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. + 0.25 + z2 = -0.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + z2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 1.25 + z2 = -0.5 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = -0.5 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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