Respuesta :

we are given

[tex] 4x^2+24x=4 [/tex]

We can see that left side is multiple of 4

so, we can factor out 4

[tex] 4(x^2+6x)=4 [/tex]

we can cancel 4

[tex] (x^2+6x)=1 [/tex]

now, we can complete square

[tex] x^2+6x+3^2=1+3^2 [/tex]

[tex] (x+3)^2=10 [/tex]

now, we can take sqrt

we will get two equations

first equations:

[tex] (x+3)=-\sqrt{10} [/tex]

[tex] x=-3-\sqrt{10} [/tex]

Second equation:

[tex] (x+3)=\sqrt{10} [/tex]

[tex] x=-3+\sqrt{10} [/tex]

so, we will get solution as

[tex] x=-3-\sqrt{10} [/tex]

[tex] x=-3+\sqrt{10} [/tex] .............Answer

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