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Simplifying 4z2 + 42z = -160 Reorder the terms: 42z + 4z2 = -160 Solving 42z + 4z2 = -160 Solving for variable 'z'. Reorder the terms: 160 + 42z + 4z2 = -160 + 160 Combine like terms: -160 + 160 = 0 160 + 42z + 4z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(80 + 21z + 2z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(80 + 21z + 2z2)' equal to zero and attempt to solve: Simplifying 80 + 21z + 2z2 = 0 Solving 80 + 21z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40 + 10.5z + z2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + 10.5z + -40 + z2 = 0 + -40 Reorder the terms: 40 + -40 + 10.5z + z2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 10.5z + z2 = 0 + -40 10.5z + z2 = 0 + -40 Combine like terms: 0 + -40 = -40 10.5z + z2 = -40 The z term is 10.5z. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5z + 27.5625 + z2 = -40 + 27.5625 Reorder the terms: 27.5625 + 10.5z + z2 = -40 + 27.5625 Combine like terms: -40 + 27.5625 = -12.4375 27.5625 + 10.5z + z2 = -12.4375 Factor a perfect square on the left side: (z + 5.25)(z + 5.25) = -12.4375 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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