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Simplifying 5z * 5z + 3z + 8z * 8z = 0 Reorder the terms for easier multiplication: 5 * 5z * z + 3z + 8z * 8z = 0 Multiply 5 * 5 25z * z + 3z + 8z * 8z = 0 Multiply z * z 25z2 + 3z + 8z * 8z = 0 Reorder the terms for easier multiplication: 25z2 + 3z + 8 * 8z * z = 0 Multiply 8 * 8 25z2 + 3z + 64z * z = 0 Multiply z * z 25z2 + 3z + 64z2 = 0 Reorder the terms: 3z + 25z2 + 64z2 = 0 Combine like terms: 25z2 + 64z2 = 89z2 3z + 89z2 = 0 Solving 3z + 89z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(3 + 89z) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(3 + 89z)' equal to zero and attempt to solve: Simplifying 3 + 89z = 0 Solving 3 + 89z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 89z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 89z = 0 + -3 89z = 0 + -3 Combine like terms: 0 + -3 = -3 89z = -3 Divide each side by '89'. z = -0.03370786517 Simplifying z = -0.03370786517Solution
z = {0, -0.03370786517}
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