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Sagot :

rvkacademic

Answer:

[tex]x = \frac{5}{3}[/tex]

Step-by-step explanation:

The expression under the square root is [tex]\sqrt{4x^2 - 20x + 25}[/tex]

This is equivalent of [tex](2x-5)^2[/tex]

We can check this by using the formula
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]

where [tex]\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\[/tex]

So

[tex]\sqrt{4x^2 - 20x + 25} = \sqrt{(2x-5)^2}[/tex] which is [tex](2x-5)[/tex]

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

So that gives us

[tex]2x - 5 = 5-2x\\[/tex]

Collecting like terms on each side gives us

[tex]2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3[/tex]

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