HELP! Consider the below equation:

0.5x-7= sqrt(-5x+29)

Give 2 different ways to show that the equation does not have any solutions. One way must be solving algebraically, and the other way must be by graphing.

Algebraically

0.5x-7= √(-5x+29)

(0.5x-7)² = -5x+29

(0.5x)² - 2*0.5x*7 + 7² = -5x+29

0.25x² - 7x + 49 + 5x - 29 = 0

0.25x² - 2x + 20 = 0

Its discriminant is:

b² - 4*a*c

(-2)² - 4*0.25*20

-16 < 0

Therefore, the equation has no solutions.

Graphically

In the picture attached, the plots of the functions are shown. We can see that they don't intersect each other, and that is why there is no solution.

1. Property

This is an example of the transitive property of equality.

2. Definition

This is the definition of a right angle.

3. Property

This is an exmaple of the division propety of equality.

4. Definition

This is the definition of a midpoint.

5. Property

This is an example of the symmetric property of equality.

Let me know if you have any questions, thanks!