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Simplifying 5z2 + 30z + -275 = 0 Reorder the terms: -275 + 30z + 5z2 = 0 Solving -275 + 30z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(-55 + 6z + z2) = 0 Factor a trinomial. 5((-11 + -1z)(5 + -1z)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-11 + -1z)' equal to zero and attempt to solve: Simplifying -11 + -1z = 0 Solving -11 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1z = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1z = 0 + 11 -1z = 0 + 11 Combine like terms: 0 + 11 = 11 -1z = 11 Divide each side by '-1'. z = -11 Simplifying z = -11Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve: Simplifying 5 + -1z = 0 Solving 5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z = 0 + -5 -1z = 0 + -5 Combine like terms: 0 + -5 = -5 -1z = -5 Divide each side by '-1'. z = 5 Simplifying z = 5Solution
z = {-11, 5}
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