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Simplifying 4z2 + 19z + 4 = 9 Reorder the terms: 4 + 19z + 4z2 = 9 Solving 4 + 19z + 4z2 = 9 Solving for variable 'z'. Reorder the terms: 4 + -9 + 19z + 4z2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + 19z + 4z2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + 19z + 4z2 = 0 Factor a trinomial. (-5 + -1z)(1 + -4z) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 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 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25Solution
z = {-5, 0.25}
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