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Simplifying (5y + -1z)(5y + -1z) = 0 Multiply (5y + -1z) * (5y + -1z) (5y * (5y + -1z) + -1z * (5y + -1z)) = 0 ((5y * 5y + -1z * 5y) + -1z * (5y + -1z)) = 0 Reorder the terms: ((-5yz + 25y2) + -1z * (5y + -1z)) = 0 ((-5yz + 25y2) + -1z * (5y + -1z)) = 0 (-5yz + 25y2 + (5y * -1z + -1z * -1z)) = 0 (-5yz + 25y2 + (-5yz + 1z2)) = 0 Reorder the terms: (-5yz + -5yz + 25y2 + 1z2) = 0 Combine like terms: -5yz + -5yz = -10yz (-10yz + 25y2 + 1z2) = 0 Solving -10yz + 25y2 + 1z2 = 0 Solving for variable 'y'. Factor a trinomial. (5y + -1z)(5y + -1z) = 0Subproblem 1
Set the factor '(5y + -1z)' equal to zero and attempt to solve: Simplifying 5y + -1z = 0 Solving 5y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 5y + -1z + z = 0 + z Combine like terms: -1z + z = 0 5y + 0 = 0 + z 5y = 0 + z Remove the zero: 5y = z Divide each side by '5'. y = 0.2z Simplifying y = 0.2zSubproblem 2
Set the factor '(5y + -1z)' equal to zero and attempt to solve: Simplifying 5y + -1z = 0 Solving 5y + -1z = 0 Move all terms containing y to the left, all other terms to the right. Add 'z' to each side of the equation. 5y + -1z + z = 0 + z Combine like terms: -1z + z = 0 5y + 0 = 0 + z 5y = 0 + z Remove the zero: 5y = z Divide each side by '5'. y = 0.2z Simplifying y = 0.2zSolution
y = {0.2z, 0.2z}
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