Скачать или смотреть A nice math problem | Olympiad Question | Gonitbidda

The tutorial demonstrates how to solve for $x$ in the equation:
$x = \sqrt{156 + x}$

*Step-by-Step Solution*

*Step 1: Square Both Sides* – To remove the radical, both sides are squared, resulting in $x^2 = 156 + x$.
*Step 2: Rearrange to Standard Form* – The equation is moved into a standard quadratic form: $x^2 - x - 156 = 0$.
*Step 3: Middle Term Factorization* – The video explains finding two numbers whose product is $-156$ and whose sum is $-1$. The factors identified are $12$ and $13$.
*Step 4: Grouping and Factoring* – The middle term is split into $-13x + 12x$. After grouping, the equation becomes $(x + 12)(x - 13) = 0$.
*Step 5: Solve for x* – This yields two potential solutions: $x = -12$ or $x = 13$.
*Step 6: Check Validity* – The video checks both answers. While $x = 13$ works, $x = -12$ is ruled out because the principal square root is always non-negative.
*Final Answer:* $x = 13$.

*Practice Problem*

At the end of the video, a homework problem is provided for viewers:
$x = \sqrt{240 + x}$