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Solve for x.
√x+3 = 2√x-2

User Biketire
by
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1 Answer

2 votes

Answer:

To solve for x, we can start by squaring both sides of the equation:

(√x+3)² = (2√x-2)²

On the left side, we have:

(√x+3)² = x + 6√x + 9

On the right side, we have:

(2√x-2)² = (2√x)² - 2(2√x)(2) + 2² = 4x - 8√x + 4

So now we have:

x + 6√x + 9 = 4x - 8√x + 4

Grouping like terms, we can simplify this to:

10√x - 3x + 5 = 0

Now we can solve for x by isolating the radical term and squaring both sides:

10√x - 3x + 5 = 0

10√x = 3x - 5

(10√x)² = (3x - 5)²

100x = 9x² - 30x + 25

Moving all the terms to one side, we get:

9x² - 130x + 25 = 0

We can now solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have:

(3x - 5)(3x - 5) = 0

So the solution is:

3x - 5 = 0

3x = 5

x = 5/3

Therefore, the solution to the equation √x+3 = 2√x-2 is x = 5/3.

Explanation:

User Waxrat
by
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