Question

Let ​ x^2+18x=44 .​ What values make an equivalent number sentence after completing the square?

PLEASE EXPLAIN

Answer 1

To find the final term to compete the square you need to divide the 'x' term by 2 then square it


`x^2 +18x + = 44+ \\ x^2+18x+( (18)/(2) )^2=44+( (18)/(2) )^2 \\ x^2+18x+9^2=44+9^2 \\ x^2+18x+81=44+81 \\ (x+9)^2=125` - equivalent equation

Answer 2

The value of x are 2.18 and -20.8.

Explanation:

Given : Equation
`x^2+18x=44`

To find : What values make an equivalent number sentence after completing the square?

Solution :

Equation
`x^2+18x-44=0`

Applying completing the square,

Step 1 - Make the coefficient of x be 1

`x^2+18x-44=0`

Step 2 - Add and subtract the square of half of the coefficient of x

i.e. square of 9

`x^2+18x-44+9^2-9^2=0`

Step 3 - Form the identity
`(a^2+2ab+b^2)=(a+b)^2`

`x^2+2.9.x+9^2-44-81`

`(x+9)^2-125=0`

Completing the square form of the given equation is
`(x+9)^2-125=0`

Now, we solve for x

`(x+9)^2=125`

`x+9=√(125)`

`x+9=\pm 11.18`

`x=\pm 11.18-9`

`x=11.18-9,-11.8-9`

`x=2.18,-20.8`

Therefore, The value of x are 2.18 and -20.8.