Question

solve this radical equation.
8-x=square root 2x+19

Answer 1

how can you get rid of the radical sign?

Answer 2

square both sides

Answer 3

x=-5

Answer 4

√(2x + 19) - 8 = x

Add both sides by 8:

√(2x + 19) = x + 8

Square both sides:

√(2x + 19)² = (x + 8)²
2x + 19 = x² + 16x + 64

Bring 2x + 19 to the right:

0 = x² + 16x + 64 - (2x + 19)
0 = x² + 16x + 64 - 2x - 19
0 = x² + 14x + 45

Factoring gives:

0 = (x + 9)(x + 5)

Setting each factor to zero, known as zero-product identity, we finally obtain:

x + 9 = 0 and x + 5 = 0
x = {-9,-5}

Check each x value to determine which one best fits the given equation:

√(2(-9) + 19) - 8 = -9
√(-18 + 19) - 8 = -9
√(1) - 8 = -9
1 - 8 = -9 (FALSE)

√(2(-5) + 19) - 8 = -5
√(-10 + 19) - 8 = -5
√(9) - 8 = -5
3 - 8 = -5 (TRUE)

Hence, x = -5

I hope this helps!

Answer 5

thanks chaser71 and jacob1233

Answer 6

np

Answer 7

no problem!