Question

What is the solution of the equation?

Answer 1

The answer is x = 7

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

Answer 2

Answer: 7

Explanation:

`√(2x-5)+4 = x`

Restriction: x ≥ 4 why? because
`√(2x-5)\geq0`

`√(2x-5)+4 = x`

-4 -4

`√(2x-5) = x - 4`

`(√(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