Question

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

Answer 1

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

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 $x=-8$