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

Mathematics

1 answer:

iragen [17]4 years ago

4 0

Answer:

x = 4 + sqrt(73) or x = 4 - sqrt(73)

Step-by-step explanation by completing the square:

Solve for x:

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

Expand out terms of the left hand side:

x^2 - 8 x - 48 = 9

Add 48 to both sides:

x^2 - 8 x = 57

Add 16 to both sides:

x^2 - 8 x + 16 = 73

Write the left hand side as a square:

(x - 4)^2 = 73

Take the square root of both sides:

x - 4 = sqrt(73) or x - 4 = -sqrt(73)

Add 4 to both sides:

x = 4 + sqrt(73) or x - 4 = -sqrt(73)

Add 4 to both sides:

Answer: x = 4 + sqrt(73) or x = 4 - sqrt(73)

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