Rewrite the function by completing the square.
f(x)=x^2+20x+40

f(x)=x²+20x+40

To complete the square, the same value needs to be added to both sides.

f(x)+?=x²+20x+?+40

Now i make the same thing in different forms ok

To complete the square x²+20x+100=(x+10)² add 100 to the expression

f(x)+?=x²+20x+100+40

Is the same ok you can choose which way you can do

x²+20x+?

write the expression as a product with the factor 2 and x

x²+2x×x10+?

x²+2×x×10+?

Since 10 is part of the middle term, add 10² to the expression

x²+2×x×10+10²

Calculate the product

x²+20x+10²

or evaluate the power

x²+20x+100

f(x) +?=x²+20x+100+40

Since 100 was added to the right - hand side, also add 100 to the left hand side

f(x)+100=x²+20x+100+40

Using a²+2ab+b²=(a+b)², factor the expression

f(x)+100=(x+10)²+40

x²+20x+100

Write the expression as a product with the factors x and 10

x²+2×x×10+100

Write the number in the exponential form with an exponent of 2

x²+2×x×10+10²

Using a²+2ab+b²=(a+b)² factor the expression

(x+10)²

f(x)+100=(x+10)²+40

Move constant to the right-hand side and change its sign

f(x)=(x+10)²+40-100

Calculate the difference

40-100

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger

-(100-40)

Subtract the numbers

-60

f(x)=(x+10)²-60

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