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Simplifying (14z2 + 2) + (3z + -4) = 0 Reorder the terms: (2 + 14z2) + (3z + -4) = 0 Remove parenthesis around (2 + 14z2) 2 + 14z2 + (3z + -4) = 0 Reorder the terms: 2 + 14z2 + (-4 + 3z) = 0 Remove parenthesis around (-4 + 3z) 2 + 14z2 + -4 + 3z = 0 Reorder the terms: 2 + -4 + 3z + 14z2 = 0 Combine like terms: 2 + -4 = -2 -2 + 3z + 14z2 = 0 Solving -2 + 3z + 14z2 = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -2z)(2 + -7z) = 0Subproblem 1
Set the factor '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 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 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 2
Set the factor '(2 + -7z)' equal to zero and attempt to solve: Simplifying 2 + -7z = 0 Solving 2 + -7z = 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 + -7z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7z = 0 + -2 -7z = 0 + -2 Combine like terms: 0 + -2 = -2 -7z = -2 Divide each side by '-7'. z = 0.2857142857 Simplifying z = 0.2857142857Solution
z = {-0.5, 0.2857142857}
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