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Simplifying 0 = z2 + -10z + 25 Reorder the terms: 0 = 25 + -10z + z2 Solving 0 = 25 + -10z + z2 Solving for variable 'z'. Combine like terms: 0 + -25 = -25 -25 + 10z + -1z2 = 25 + -10z + z2 + -25 + 10z + -1z2 Reorder the terms: -25 + 10z + -1z2 = 25 + -25 + -10z + 10z + z2 + -1z2 Combine like terms: 25 + -25 = 0 -25 + 10z + -1z2 = 0 + -10z + 10z + z2 + -1z2 -25 + 10z + -1z2 = -10z + 10z + z2 + -1z2 Combine like terms: -10z + 10z = 0 -25 + 10z + -1z2 = 0 + z2 + -1z2 -25 + 10z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -25 + 10z + -1z2 = 0 Factor a trinomial. (-5 + z)(5 + -1z) = 0Subproblem 1
Set the factor '(-5 + z)' equal to zero and attempt to solve: Simplifying -5 + z = 0 Solving -5 + z = 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 + z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + z = 0 + 5 z = 0 + 5 Combine like terms: 0 + 5 = 5 z = 5 Simplifying z = 5Subproblem 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 = {5, 5}
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