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Simplifying 4z + -5 = 9 + 2z(z + 1) Reorder the terms: -5 + 4z = 9 + 2z(z + 1) Reorder the terms: -5 + 4z = 9 + 2z(1 + z) -5 + 4z = 9 + (1 * 2z + z * 2z) -5 + 4z = 9 + (2z + 2z2) Solving -5 + 4z = 9 + 2z + 2z2 Solving for variable 'z'. Reorder the terms: -5 + -9 + 4z + -2z + -2z2 = 9 + 2z + 2z2 + -9 + -2z + -2z2 Combine like terms: -5 + -9 = -14 -14 + 4z + -2z + -2z2 = 9 + 2z + 2z2 + -9 + -2z + -2z2 Combine like terms: 4z + -2z = 2z -14 + 2z + -2z2 = 9 + 2z + 2z2 + -9 + -2z + -2z2 Reorder the terms: -14 + 2z + -2z2 = 9 + -9 + 2z + -2z + 2z2 + -2z2 Combine like terms: 9 + -9 = 0 -14 + 2z + -2z2 = 0 + 2z + -2z + 2z2 + -2z2 -14 + 2z + -2z2 = 2z + -2z + 2z2 + -2z2 Combine like terms: 2z + -2z = 0 -14 + 2z + -2z2 = 0 + 2z2 + -2z2 -14 + 2z + -2z2 = 2z2 + -2z2 Combine like terms: 2z2 + -2z2 = 0 -14 + 2z + -2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + z + -1z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + z + -1z2)' equal to zero and attempt to solve: Simplifying -7 + z + -1z2 = 0 Solving -7 + z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -1z + z2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -1z + -7 + z2 = 0 + -7 Reorder the terms: 7 + -7 + -1z + z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z + z2 = 0 + -7 -1z + z2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1z + z2 = -7 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. -1z + 0.25 + z2 = -7 + 0.25 Reorder the terms: 0.25 + -1z + z2 = -7 + 0.25 Combine like terms: -7 + 0.25 = -6.75 0.25 + -1z + z2 = -6.75 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = -6.75 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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