When you take the square root of $100$, do you get only one value, or should you consider both a positive and a negative value?

After you turn the problem into two simple linear equations (one with $+10$ and one with $-10$), solve both and then decide which solution is greater.

In Desmos, enter y = (x + 4)^2 on one line and y = 100 on another line. You will see a parabola and a horizontal line.

Click on each point where the parabola and the horizontal line intersect. Desmos will show the coordinates of these intersection points; note both $x$-values.

Compare the two $x$-values from the intersection points and choose the greater one; that $x$-value is the larger solution to the equation.

Start from the equation

To undo the square, take the square root of both sides. Remember that the square root of a positive number has two values, positive and negative:

This means $x + 4$ can be either $10$ or $-10$.

From $|x+4| = 10$, write the two equations:

1. $x + 4 = 10$
2. $x + 4 = -10$

Now isolate $x$ in each:

• For $x + 4 = 10$: subtract 4 from both sides to get $x = 10 - 4$.
• For $x + 4 = -10$: subtract 4 from both sides to get $x = -10 - 4$.

These give two candidate values for $x$; evaluate and compare them in the next step.

The problem asks for the larger solution.

Compute the values: $10 - 4 = 6$ and $-10 - 4 = -14$. Compare them: $6$ is greater than $-14$.

So, the larger solution is 6.