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Simplifying 10z2 = z + 3 Reorder the terms: 10z2 = 3 + z Solving 10z2 = 3 + z Solving for variable 'z'. Reorder the terms: -3 + -1z + 10z2 = 3 + z + -3 + -1z Reorder the terms: -3 + -1z + 10z2 = 3 + -3 + z + -1z Combine like terms: 3 + -3 = 0 -3 + -1z + 10z2 = 0 + z + -1z -3 + -1z + 10z2 = z + -1z Combine like terms: z + -1z = 0 -3 + -1z + 10z2 = 0 Factor a trinomial. (-1 + -2z)(3 + -5z) = 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 '(3 + -5z)' equal to zero and attempt to solve: Simplifying 3 + -5z = 0 Solving 3 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5z = 0 + -3 -5z = 0 + -3 Combine like terms: 0 + -3 = -3 -5z = -3 Divide each side by '-5'. z = 0.6 Simplifying z = 0.6Solution
z = {-0.5, 0.6}
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