Question 949·Easy·Math

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The equation is

(x + 4)^2 = 100

What is the larger solution to this equation?

Your answer

A parabola is the U-shaped graph of a squared expression; a horizontal line can meet it in two places. Graph both sides of the equation in Desmos and click their intersections, where the graphs meet. The rightmost intersection has the larger $x$ -coordinate. Don’t mistake the height they share for a solution.

Hints

Hint 1
A parabola is the U-shaped graph of a squared expression. A horizontal line can meet it on both sides of its lowest point. How could you graph both sides of the equation to see those meeting points?
Hint 2
An intersection is a point where two graphs meet, so its $x$ -coordinate makes both sides of the equation equal. Which intersection is farther right, and what does that tell you about the solutions?

Step-by-step

Approach 1: Graph both sides in Desmos

Step 1
Graph the squared expression
Type $y=(x+4)^2$ . Desmos shows a U-shaped graph called a parabola.
Step 2
Read the larger solution
Add $y=100$ and click both intersections. Desmos shows $(-14,100)$ and $(6,100)$ . Their $x$ -coordinates solve the equation because the two sides equal $100$ there. Read the $x$ -coordinate of the rightmost intersection, not the height they share. The larger solution is $6$ . Grid in 6.

Approach 2: Keep both signs when taking square roots

Step 1
Take the square root
Both $10^2$ and $(-10)^2$ equal $100$ , so taking a square root here requires both signs. Take the square root of each side:
$x+4=\pm10.$
Step 2
Isolate $x$
The equation gives values for $x+4$ , not $x$ . Subtract $4$ from both sides, keeping both signs:
$x=-4\pm10.$
Step 3
Choose the larger value
Adding $10$ gives the larger value. Evaluate that branch: $x=-4+10=6$ . So the larger solution is $6$ . Grid in 6.

Question 949·Easy·Math

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