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Simplifying 5z + -2z2 + 15 = 8 Reorder the terms: 15 + 5z + -2z2 = 8 Solving 15 + 5z + -2z2 = 8 Solving for variable 'z'. Reorder the terms: 15 + -8 + 5z + -2z2 = 8 + -8 Combine like terms: 15 + -8 = 7 7 + 5z + -2z2 = 8 + -8 Combine like terms: 8 + -8 = 0 7 + 5z + -2z2 = 0 Factor a trinomial. (7 + -2z)(1 + z) = 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 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {3.5, -1}
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