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Simplifying 4z2 + 10z = 14z + -4 Reorder the terms: 10z + 4z2 = 14z + -4 Reorder the terms: 10z + 4z2 = -4 + 14z Solving 10z + 4z2 = -4 + 14z Solving for variable 'z'. Reorder the terms: 4 + 10z + -14z + 4z2 = -4 + 14z + 4 + -14z Combine like terms: 10z + -14z = -4z 4 + -4z + 4z2 = -4 + 14z + 4 + -14z Reorder the terms: 4 + -4z + 4z2 = -4 + 4 + 14z + -14z Combine like terms: -4 + 4 = 0 4 + -4z + 4z2 = 0 + 14z + -14z 4 + -4z + 4z2 = 14z + -14z Combine like terms: 14z + -14z = 0 4 + -4z + 4z2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -1z + z2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1z + z2)' equal to zero and attempt to solve: Simplifying 1 + -1z + z2 = 0 Solving 1 + -1z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1z + -1 + z2 = 0 + -1 Reorder the terms: 1 + -1 + -1z + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z + z2 = 0 + -1 -1z + z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1z + z2 = -1 The z term is -1z. 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 = -1 + 0.25 Reorder the terms: 0.25 + -1z + z2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1z + z2 = -0.75 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = -0.75 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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