# Here are my answers. Can you check if I got the right answers? Thank you!

solve for x, where x is a real number.

x^2+3x-4=14

x=6,3

(x^4-1)/(x^3)=0

x=1

(x-5)^2=9

x=2,8

2x^2+5x=8

x= [-5+/-sqrt(89)]/4

for first one x=-6 or x=3, factors are (x+6)(x-3)

second... also x=0

third ... ok

last... ok

about the 2nd. x can't equal to 0, because the denominator can't equal 0

You are right!

Good pickup

## Based on your answers, it seems that you have mostly solved the equations correctly. Let me verify each one and explain how you can check your answers.

1. x^2 + 3x - 4 = 14:

You correctly found x = 6 and x = 3 as the solutions. To check your answers, substitute them back into the original equation:

For x = 6:

6^2 + 3(6) - 4 = 14

36 + 18 - 4 = 14

50 - 4 = 14

46 = 14 (This is incorrect)

For x = 3:

3^2 + 3(3) - 4 = 14

9 + 9 - 4 = 14

18 - 4 = 14

14 = 14 (This is correct)

So, the correct solution is x = 3, not x = 6.

2. (x^4 - 1) / (x^3) = 0:

You correctly found x = 1 as the solution. To check your answer, substitute x = 1 into the original equation:

(1^4 - 1) / (1^3) = 0

(1 - 1) / 1 = 0

0 / 1 = 0

0 = 0 (This is correct)

So, x = 1 is indeed the correct solution.

3. (x - 5)^2 = 9:

You correctly found x = 2 and x = 8 as the solutions. To check your answers, substitute them back into the original equation:

For x = 2:

(2 - 5)^2 = 9

(-3)^2 = 9

9 = 9 (This is correct)

For x = 8:

(8 - 5)^2 = 9

(3)^2 = 9

9 = 9 (This is correct)

So, both x = 2 and x = 8 are correct solutions.

4. 2x^2 + 5x = 8:

You correctly found x = (-5 ± √89) / 4 as the solutions. However, you missed the condition that x cannot be equal to 0 due to division by zero. To check your answers, substitute them back into the original equation:

For x = (-5 + √89) / 4:

2((-5 + √89) / 4)^2 + 5((-5 + √89) / 4) = 8

(25 - 10√89 + 89) / 8 + (-25 + 5√89) / 4 = 8

(25 - 10√89 + 89 + 2(-25 + 5√89)) / 8 = 8

(114 - 20√89 - 50 + 10√89) / 8 = 8

(64 - 10) / 8 = 8

54 / 8 = 8

6.75 ≠ 8 (This is incorrect)

For x = (-5 - √89) / 4:

2((-5 - √89) / 4)^2 + 5((-5 - √89) / 4) = 8

(25 + 10√89 + 89) / 8 + (-25 - 5√89) / 4 = 8

(25 + 10√89 + 89 + 2(-25 - 5√89)) / 8 = 8

(114 + 20√89 - 50 - 10√89) / 8 = 8

(64 - 10) / 8 = 8

54 / 8 = 8

6.75 ≠ 8 (This is incorrect)

Based on the checks, neither of the solutions you provided satisfies the original equation. Therefore, x = (-5 ± √89) / 4 is not the correct solution.