Question

Which of the following are solutions to the equation below x^2+8x+16=2

Answer 1

`x_(1) =-4+√(2) \\x_(2) =-4-√(2) \\`

Explanation:

Using quadratic formula:

`\frac{-b+-\sqrt{b^(2) -4*a*c} }{2*a}`

We will have 2 solutions.

x^2+8x+16=2

x^2+8x+14=0

a= 1 b=8 c= 14

`x_(1)= \frac{-8+\sqrt{8^(2)-4*1*14} }{2*1} \\\\x_(2)= \frac{-8-\sqrt{8^(2)-4*1*14} }{2*1} \\`

We can write:

`x_(1)= \frac{-8+\sqrt{{64}-56} }{2} \\\\x_(2)= \frac{-8-\sqrt{{64}-56} }{2} \\`

`x_(1)= -4+\frac{\sqrt{{64}-56} }{2} \\\\x_(2)= -4-\frac{\sqrt{{64}-56} }{2} \\`

so, we have:

`x_(1)= -4+\frac{\sqrt{{}8} }{2} \\\\x_(2)=-4-\frac{\sqrt{{}8} }{2} \\`

simplifying we have:

`x_(1)= -4+\frac{\sqrt{{}2*4} }{2} \\\\x_(2)= -4-\frac{\sqrt{{}2*4} }{2} \\`

Finally:

`x_(1)= -4+√(2) \\\\x_(2)= -4-√(2) \\`