Question

Solve the radical equation. 25-40x = x – 10 Which is the true solution? –15 –5 There are no true solutions. Both –5 and –15 and are true solutions.

Answer 1

√(25-40x) = x – 10


Square both sides


25 - 40x = x² – 20x + 100


Rearrange

x² +20x + 75  = 0


x² + 5x + 15x + 75 = 0


x(x + 5) + 15(x + 5) = 0


(x + 15)(x + 5) = 0


Either (x + 15) = 0


                    x = -15


Or


x + 5 = 0

x = -5


Both –5 and –15 and are true solutions

Answer 2

Answer:

Step-by-step explanation:

√(25-40x) = x – 10

Square both sides

25 - 40x = x² – 20x + 100

Rearrange

x² +20x + 75 = 0

x² + 5x + 15x + 75 = 0

x(x + 5) + 15(x + 5) = 0

(x + 15)(x + 5) = 0

Either (x + 15) = 0

x = -15

Or

x + 5 = 0

x = -5

Both –5 and –15 and are true solutions