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Solving Equation: 2√x - 14 = 288/√x
Published on September 3, 2024
Algebra
Solve the equation 2√x - 14 = 288/√x step-by-step using the quadratic formula. The solution is x = 256.
Question
Answer
Let’s solve this equation step by step:
-
The equation given is:
-
Let’s start by multiplying both sides by
to eliminate the fraction on the right side: -
Now, let’s rearrange the equation to standard form:
-
This is a quadratic equation in terms of
. Let’s substitute : -
Now we can solve this using the quadratic formula:
Where, , and -
Plugging into the quadratic formula:
-
Simplifying:
-
This gives us two solutions:
or -
Remember that
, so . Since we can’t have a negative square root, we only consider the positive solution:
Therefore, the solution to the equation is