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Simplifying z2 + 23z = 50 Reorder the terms: 23z + z2 = 50 Solving 23z + z2 = 50 Solving for variable 'z'. Reorder the terms: -50 + 23z + z2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 23z + z2 = 0 Factor a trinomial. (-25 + -1z)(2 + -1z) = 0Subproblem 1
Set the factor '(-25 + -1z)' equal to zero and attempt to solve: Simplifying -25 + -1z = 0 Solving -25 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1z = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1z = 0 + 25 -1z = 0 + 25 Combine like terms: 0 + 25 = 25 -1z = 25 Divide each side by '-1'. z = -25 Simplifying z = -25Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {-25, 2}
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