Question

What is the solution of the equation?

Answer 1

Answer: 7

Step-by-step explanation:

$\sqrt{2x-5}+4 = x$

Restriction: x ≥ 4  why? because $\sqrt{2x-5}\geq0$

$\sqrt{2x-5}+4 = x$

            -4     -4  

$\sqrt{2x-5} = x - 4$

$(\sqrt{2x-5})^2 = (x - 4)^2$

2x - 5 = x² - 8x + 16

-2x +5        -2x   +5  

       0 = x² - 10x + 21

       0 = (x - 3) (x - 7)

0 = x - 3        0 = x - 7

3 = x              $\big{\boxed{7=x}}$

  ↓

not valid

Answer 2

Answer:

The answer is x = 7

Step-by-step explanation:

√2x − 5 + 4 = x

= √2x − 5 + 4 + − 4 = x + −4  (add -4 to both sides)

=√2x − 5 = x − 4

=√2x−5=x−4

2x−5=(x−4)2 (Square both sides)

2x−5=x2−8x+16

2x−5−(x2−8x+16)=x2−8x+16−(x2−8x+16)(Subtract x^2-8x+16 from both sides)

−x2+10x−21=0

(−x+3)(x−7)=0 (Factor left side of equation)

−x+3=0 or x−7=0 (Set factors equal to 0)

x=3 or x=7