Question

What are the solution(s) to the quadratic equation 50 – x2 = 0?

Answer 1

For this case we must solve the following quadratic equation:

$50-x ^ 2 = 0$

Subtracting 50 from both sides of the equation we have:

$-x ^ 2 = -50\\x ^ 2 = 50$

Applying square root to both sides of the equation we have:

$x = \pm \sqrt {50}\\x = \pm \sqrt {25 * 2}\\x = \pm \sqrt {5 ^ 2 * 2}\\x = \pm5 \sqrt {2}$

We have two real roots:

$x_ {1} = 5 \sqrt {2}\\x_ {2} = - 5 \sqrt {2}$

ANswer:

$x_ {1} = 5 \sqrt {2}\\x_ {2} = - 5 \sqrt {2}$