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Simplifying 25z4 + 7z3 + 4z2 = 0 Reorder the terms: 4z2 + 7z3 + 25z4 = 0 Solving 4z2 + 7z3 + 25z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z2'. z2(4 + 7z + 25z2) = 0Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(4 + 7z + 25z2)' equal to zero and attempt to solve: Simplifying 4 + 7z + 25z2 = 0 Solving 4 + 7z + 25z2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.16 + 0.28z + z2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + 0.28z + -0.16 + z2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + 0.28z + z2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + 0.28z + z2 = 0 + -0.16 0.28z + z2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 0.28z + z2 = -0.16 The z term is 0.28z. Take half its coefficient (0.14). Square it (0.0196) and add it to both sides. Add '0.0196' to each side of the equation. 0.28z + 0.0196 + z2 = -0.16 + 0.0196 Reorder the terms: 0.0196 + 0.28z + z2 = -0.16 + 0.0196 Combine like terms: -0.16 + 0.0196 = -0.1404 0.0196 + 0.28z + z2 = -0.1404 Factor a perfect square on the left side: (z + 0.14)(z + 0.14) = -0.1404 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.Solution
z = {0}
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