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

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

we are given

We can see that left side is multiple of 4

so, we can factor out 4

we can cancel 4

now, we can complete square

now, we can take sqrt

we will get two equations

first equations:

Second equation:

so, we will get solution as

.............Answer

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