Answer:
(x + 6)² = 40 → x = ±2√10 - 6
Step-by-step 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 [tex](\frac{b}{2} )^2}[/tex]
In this case, our b is 12, so plugging this into the formula we get [tex](\frac{12}{2} )^{2} =6^{2} =36[/tex]
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 [tex]\sqrt{(x+6)^{2} } =\sqrt{40}[/tex] to get x + 6 = ±2√10
Then we need to subtract 6 from both sides to get x = ±2√10 - 6
