Question

X squared + 12x +3 = 7 solve by completing the square

Answer 1

(x + 6)² = 40 → x = ±2√10 - 6

Explanation:

x²+12x+3=7 can be solved by completing the square

To do so we must first find the term we are adding to both sides of the equation by using
`((b)/(2) )^2}`

In this case, our b is 12, so plugging this into the formula we get
`((12)/(2) )^(2) =6^(2) =36`

We first need to subtract the 3 from both sides of the equation to get x²+12x=4

We then can add the 36 to both sides of the equation: x² + 12x + 36 = 4 + 36 → x² +12x + 36 = 40

Now we are able to factor the left side of the equation to get (x + 6)² = 40

To solve for x we need to take the square root of both sides
`\sqrt{(x+6)^(2) } =√(40)` to get x + 6 = ±2√10

Then we need to subtract 6 from both sides to get x = ±2√10 - 6

Answer 2

x = -6 ± 2sqrt(10)

Explanation:

x^2 + 12x+3 = 7

Subtract 3 from each side

x^2 +12x = 4

Take the coefficient of x

12

Divide by 2

12/2 = 6

Square it

6^2 =36

Add this to each side

x^2 +12x +36 = 4+36

(x+6)^2 = 40

Take the square root of each side

sqrt((x+6)^2) =± sqrt(40)

x+6 = ± sqrt(40)

x+6 = ± sqrt(4)sqrt(10)

x+6 =± 2sqrt(10)

Subtract 6 from each side

x+6-6 = -6 ± 2sqrt(10)

x = -6 ± 2sqrt(10)