Question

Complete the square to solve 4x^2+24x=4.

Answer 1

4x^2+24x=4

Step 1:

make the coefficient of x² as 1, divide both sides by 4

x² +6x =1

Step 2:

take half of coefficient of x, square it and add it to both sides

half of 6 is 3 and 3²=9, so add 9 to both sides

x² +6x+9=1+9

x²+6x+3²=10

(x+3)²=10

now when we take square root we will get both + and - √10 on right side

x+3= +√10

x+3=-√10

solving for x

x=+√10-3

x=-√10-3

Answer 2

we are given

`4x^2+24x=4`

We can see that left side is multiple of 4

so, we can factor out 4

`4(x^2+6x)=4`

we can cancel 4

`(x^2+6x)=1`

now, we can complete square

`x^2+6x+3^2=1+3^2`

`(x+3)^2=10`

now, we can take sqrt

we will get two equations

first equations:

`(x+3)=-√(10)`

`x=-3-√(10)`

Second equation:

`(x+3)=√(10)`

`x=-3+√(10)`

so, we will get solution as

`x=-3-√(10)`

`x=-3+√(10)` .............Answer