Question

Solve the quadratic equation by completing the square. x2 + 6x + 7 = 0

Answer 1

 from the equation  x^2 - 6x + 7 = 0 , b is equal to -6. The form should become y = (x-(b/2)^2) + c. (b/2)^2 is equal to 9. Hence,

0 = (x - 3)^2 -9 + 7 
0 = (x - 3)^2 -2
2 = (x - 3)^2

x should be equal to -1.5858 and -4.4142

Answer 2

Answer:

x1 = -1.59

x2 = -4.41

Step-by-step explanation:

The quadratic equation is of the form

$ax^{2}+bx+c=0$

In the given case, b = 6

We apply the formula

$(\frac{b}{2})^{2}=(\frac{6}{2})^{2}=3^{2}=9$

$x^{2}+6x+7+9-9=0$

$x^{2}+6x+9+7-9=0$

$(x^{2}+6x+9)-2=0$

$(x+3)(x-3)=2$

$(x+3)^{2}=2$

Applying square root to both parts of the equation, we get,

$\sqrt{(x+3)^{2}} =\sqrt{2}$

$x+3=\sqrt{2}$

$x=\sqrt{2}-3$

x = ± 1.41 - 3

"x" then has two values:

x1 = 1.41 - 3 = -1.59

x2 = -1.41 - 3 = -4.41

Hope this helps!