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Simplifying 10z2 + 37z + 7 = 0 Reorder the terms: 7 + 37z + 10z2 = 0 Solving 7 + 37z + 10z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + 2z)(1 + 5z) = 0Subproblem 1
Set the factor '(7 + 2z)' equal to zero and attempt to solve: Simplifying 7 + 2z = 0 Solving 7 + 2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2z = 0 + -7 2z = 0 + -7 Combine like terms: 0 + -7 = -7 2z = -7 Divide each side by '2'. z = -3.5 Simplifying z = -3.5Subproblem 2
Set the factor '(1 + 5z)' equal to zero and attempt to solve: Simplifying 1 + 5z = 0 Solving 1 + 5z = 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 + 5z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5z = 0 + -1 5z = 0 + -1 Combine like terms: 0 + -1 = -1 5z = -1 Divide each side by '5'. z = -0.2 Simplifying z = -0.2Solution
z = {-3.5, -0.2}
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