Solution for some variable is its value(s) for which the considered statement holds true. The solution of given equation is x =8, or x = -8
How to solve an algebraic equation?
Sometimes it is possible to solve it, sometimes there are no solutions.
Usually, there are methods developed for most of the types of algebraic equation one can counter. They all try to find the values of variables for which the equation or the considered mathematical statement holds true.
For the given case, the equation we've got is
[tex]x^2 - 9 = 55[/tex]
We can think of doing transfer of 9 on right side, then taking square root of both the sides.
Doing so, we get:
[tex]x^2 - 9 = 55\\x^2 = 55 + 9 = 64\\\\\text{Taking roots of both the sides}\\\\\pm\sqrt{x^2} = \pm\sqrt{64}\\\pm x = \pm 8 \implies x = 8, x = -8[/tex]
(square root of a positive quantity can be of either sign(+ve or -ve) ).
Thus, the solution of given equation is x =8, or x = -8
Learn more about solutions of quadratic equations here:
https://brainly.com/question/3358603
