Solve for x: x² = (20-x)*10/2

Published on September 2, 2024

Algebra

Solve the quadratic equation x² = (20-x)*10/2. The solutions are x = (-5 ± 5√17)/2, approximately x ≈ 8.09 or x ≈ -13.09.

Question

x^2=(20-x)*10/2 Solve x=

Answer

Let’s solve this step by step:

First, let’s simplify the right side of the equation:
Now, let’s expand the right side:
Let’s rearrange the equation to standard form:
This is a quadratic equation. We can solve it using the quadratic formula:

Where , , and
Let’s substitute these values into the quadratic formula:
Simplify under the square root:
Simplify :
So our solution is:
We can simplify this further:

Therefore, the solutions are:

We can approximate these values:

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