Question

Solve for xxx. Write the smaller solution first, and the larger solution second. Round to two decimal places. (x + 3)^2 - 3 = 0

Answer 1

x=-4.73 and -1.26

Explanation:

We need to solve the given equation for x.

`(x + 3)^2 - 3 =0`

Solving the above equation using formula (a+b)² =a²+2ab+b²

`(x + 3)^2 - 3 =0\\\\x^2+9+6x-3=0\\\\x^2+6x+6=0`

It is a quadratic equation.

`x=(-b\pm √(b^2-4ac) )/(2a)`

We have, a = 1, b = 6 and c = 6

`x=(-6\pm √((6)^2-4* 1* 6) )/(2* 1)\\\\x=\frac{-6+\sqrt{(6)^(2)-4*1*6}}{2*1},\frac{-6-\sqrt{(6)^(2)-4*1*6}}{2*1}\\\\x=-1.267, -4.73`

So, the values of x are -4.73 and -1.26