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Simplifying 0 = 40z + 100 + 4z2 Reorder the terms: 0 = 100 + 40z + 4z2 Solving 0 = 100 + 40z + 4z2 Solving for variable 'z'. Combine like terms: 0 + -100 = -100 -100 + -40z + -4z2 = 100 + 40z + 4z2 + -100 + -40z + -4z2 Reorder the terms: -100 + -40z + -4z2 = 100 + -100 + 40z + -40z + 4z2 + -4z2 Combine like terms: 100 + -100 = 0 -100 + -40z + -4z2 = 0 + 40z + -40z + 4z2 + -4z2 -100 + -40z + -4z2 = 40z + -40z + 4z2 + -4z2 Combine like terms: 40z + -40z = 0 -100 + -40z + -4z2 = 0 + 4z2 + -4z2 -100 + -40z + -4z2 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 -100 + -40z + -4z2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(25 + 10z + z2) = 0 Factor a trinomial. -4((5 + z)(5 + z)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Subproblem 2
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Solution
z = {-5, -5}
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