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
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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
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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
Answer:f(x)=(x+10)²-60
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