Use completing the square to solve for x in the equation (x-12)(x+4x)=9.

x = 6 + 3 sqrt(21/5) or x = 6 - 3 sqrt(21/5)

Step-by-step explanation:

Solve for x over the real numbers:

(x - 12) (x + 4 x) = 9

(x - 12) (x + 4 x) = 5 x (x - 12):

5 x (x - 12) = 9

Divide both sides by 5:

x (x - 12) = 9/5

Expand out terms of the left hand side:

x^2 - 12 x = 9/5

Add 36 to both sides:

x^2 - 12 x + 36 = 189/5

Write the left hand side as a square:

(x - 6)^2 = 189/5

Take the square root of both sides:

x - 6 = 3 sqrt(21/5) or x - 6 = -3 sqrt(21/5)

Add 6 to both sides:

x = 6 + 3 sqrt(21/5) or x - 6 = -3 sqrt(21/5)

Add 6 to both sides:

x = 6 + 3 sqrt(21/5) or x = 6 - 3 sqrt(21/5)

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Step-by-step explanation: