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Simplifying 21z2 + -70z + 49 = 0 Reorder the terms: 49 + -70z + 21z2 = 0 Solving 49 + -70z + 21z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '7'. 7(7 + -10z + 3z2) = 0 Factor a trinomial. 7((1 + -1z)(7 + -3z)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Subproblem 2
Set the factor '(7 + -3z)' equal to zero and attempt to solve: Simplifying 7 + -3z = 0 Solving 7 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3z = 0 + -7 -3z = 0 + -7 Combine like terms: 0 + -7 = -7 -3z = -7 Divide each side by '-3'. z = 2.333333333 Simplifying z = 2.333333333Solution
z = {1, 2.333333333}
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