Question

Help me please :)




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Answer 1

`x = (5)/(3)`

Explanation:

The expression under the square root is
`√(4x^2 - 20x + 25)`

This is equivalent of
`(2x-5)^2`

We can check this by using the formula

`(a+b)^2 = a^2 + 2ab + b^2`

where
`\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\`

So

`√(4x^2 - 20x + 25) = √((2x-5)^2)` which is
`(2x-5)`

(The square root of the square of an expression is the expression itself)

So that gives us

`2x - 5 = 5-2x\\`

Collecting like terms on each side gives us

`2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3`