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Simplifying 4z2 + 7z + -2 = 0 Reorder the terms: -2 + 7z + 4z2 = 0 Solving -2 + 7z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -1z)(1 + -4z) = 0Subproblem 1
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 = -2Subproblem 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 = {-2, 0.25}
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