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Solve for x in the equation (9x/2) = √(4x)
Published on October 22, 2024
Algebra
The equation was solved by simplifying the square root, isolating the square root term, squaring both sides, moving all terms to one side, factoring out a common factor, and solving for x, resulting in two solutions: x = 0 and x = 16/81.
Question
Answer
Let’s solve the equation step-by-step:
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Simplify the square root:
The square root of 4x can be simplified as √4x = 2√x -
Rewrite the equation:
Now our equation looks like this:
$ \frac{9x}{2} = 2\sqrt{x} $ -
Isolate the square root:
Multiply both sides of the equation by:
$ \frac{2}{9} \cdot \frac{9x}{2} = \frac{2}{9} \cdot 2\sqrt{x} $
This simplifies to:
$ x = \frac{4}{9}\sqrt{x} $ -
Square both sides:
To get rid of the square root, square both sides of the equation:
$ (x)^2 = (\frac{4}{9}\sqrt{x})^2 $
This gives us:
$ x^2 = \frac{16}{81}x $ -
Move all terms to one side:
Subtractfrom both sides:
$ x^2 - \frac{16}{81}x = 0 $ -
Factor out a common factor:
Factor out an ‘x’ from the left side:
$ x(x - \frac{16}{81}) = 0 $ -
Solve for x:
Now we have two possible solutions:-
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which means
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Therefore, the solutions to the equation are