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Simplifying 4z2 + 24z = -160 Reorder the terms: 24z + 4z2 = -160 Solving 24z + 4z2 = -160 Solving for variable 'z'. Reorder the terms: 160 + 24z + 4z2 = -160 + 160 Combine like terms: -160 + 160 = 0 160 + 24z + 4z2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(40 + 6z + z2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(40 + 6z + z2)' equal to zero and attempt to solve: Simplifying 40 + 6z + z2 = 0 Solving 40 + 6z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 6z + -40 + z2 = 0 + -40 Reorder the terms: 40 + -40 + 6z + z2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 6z + z2 = 0 + -40 6z + z2 = 0 + -40 Combine like terms: 0 + -40 = -40 6z + z2 = -40 The z term is 6z. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6z + 9 + z2 = -40 + 9 Reorder the terms: 9 + 6z + z2 = -40 + 9 Combine like terms: -40 + 9 = -31 9 + 6z + z2 = -31 Factor a perfect square on the left side: (z + 3)(z + 3) = -31 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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