Question

X^2+6x-16=0 solve each equation by completing the square

Answer 1

The solution of the equation is
`x=2` and
`x=-8`

Step-by-step explanation:

Given that the equation is
`x^(2)+6 x-16=0`

We need to determine the solution of the equation by completing the square.

Thus, we have,

`x^(2)+6 x-16=0`

Adding both sides of the equation by 16, we get,

`x^(2)+6 x=16`

Let us solve by completing the square.

To bring the equation in the form of
`x^(2)+2 a x+a^(2)=(x+a)^(2)`, let us add
`a^(2)=3^(2)` to both of the equations.

Thus, we have,

`x^(2)+6 x+3^(2)=16+3^(2)`

Simplifying, we get,

`(x+3)^(2)=25`

Taking square root on both sides of the equation, we get,

`x+3=\pm5`

Thus, the two solutions of the quadratic equation are

`x+3=5` and
`x+3=-5`

Simplifying the two values, we get,

`x=2` and
`x=-8`

Thus, the roots of the equation are
`x=2` and
`x=-8`