Question

How do you solve `(x+5)^2-7=2x+6` graphically?

Answer 1

Find the point(s) where the graph of the LHS intersects the graph of the RHS. `x= -6 or -2`

Explanation:

`(x+5)^2-7=2x+6`

The graphic below shows the graph of the parabola `y=(x+5)^2-7` and the straight line `y=2x+6`

graph{(-y+(x+5)^2-7)(-y+2x+6)=0 [-16.02, 16.02, -8.01, 8.01]}

The points of intersection are:`(-6,-6) and (-2,+2)`

Hence; `x= -6 or -2` are solutions of the equation.

[FYI: The values of the LHS are RHS are `-6 and +2` respectively at the points of intersection.]