(11𝑎 - 2)^2 - 4(-𝑎 - 5)(12𝑎 - 25) = 0

Let's expand both sides of the equation:

(11𝑎 - 2)^2 = (11𝑎 - 2)(11𝑎 - 2) Expanding using FOIL method: = 11𝑎 * 11𝑎 + 11𝑎 * (-2) + (-2) * 11𝑎 + (-2) * (-2) = 121𝑎^2 - 22𝑎 - 22𝑎 + 4 = 121𝑎^2 - 44𝑎 + 4

• 4(-𝑎 - 5)(12𝑎 - 25) = -4 * (-𝑎 * 12𝑎 - 𝑎 * (-25) - 5 * 12𝑎 + 5 * 25) = -4 * (-12𝑎^2 + 25𝑎 - 60𝑎 + 125) = -4 * (-12𝑎^2 - 35𝑎 + 125) = 48𝑎^2 + 140𝑎 - 500

Now, substitute these expanded expressions back into the original equation:

121𝑎^2 - 44𝑎 + 4 - 48𝑎^2 - 140𝑎 + 500 = 0 Combine like terms: 73𝑎^2 - 184𝑎 + 504 = 0

This is the simplified form of the given equation.