50z^2=18-25z

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Solution for 50z^2=18-25z equation:


Simplifying
50z2 = 18 + -25z

Solving
50z2 = 18 + -25z

Solving for variable 'z'.

Reorder the terms:
-18 + 25z + 50z2 = 18 + -25z + -18 + 25z

Reorder the terms:
-18 + 25z + 50z2 = 18 + -18 + -25z + 25z

Combine like terms: 18 + -18 = 0
-18 + 25z + 50z2 = 0 + -25z + 25z
-18 + 25z + 50z2 = -25z + 25z

Combine like terms: -25z + 25z = 0
-18 + 25z + 50z2 = 0

Factor a trinomial.
(-9 + -10z)(2 + -5z) = 0

Subproblem 1

Set the factor '(-9 + -10z)' equal to zero and attempt to solve: Simplifying -9 + -10z = 0 Solving -9 + -10z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -10z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10z = 0 + 9 -10z = 0 + 9 Combine like terms: 0 + 9 = 9 -10z = 9 Divide each side by '-10'. z = -0.9 Simplifying z = -0.9

Subproblem 2

Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 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 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4

Solution

z = {-0.9, 0.4}

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